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• 1.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Machine Elements.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Homogenization of a Reynolds equation describing compressible flow2012In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 390, no 2, p. 456-471Article in journal (Refereed)

We homogenize a Reynolds equation with rapidly oscillating film thickness function hε, assuming a constant compressiblity factor in the pressure-density relation. The oscillations are due to roughness on the bounding surfaces of the fluid film. As shown by previous studies, homogenization is an effective approach for analyzing the effects of surface roughness in hydrodynamic lubrication. By two-scale convergence theory we obtain the limit problem (homogenized equation) and strong convergence in L2 for the unknown density ρε. By adding a small corrector term we also obtain strong convergence in the Sobolev norm.

• 2. Astashkin, Sergey
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Ultrasymmetric Orlicz spaces2008In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 347, no 1, p. 273-285Article in journal (Refereed)

It is proved that ultrasymmetric reflexive Orlicz spaces can be described exactly as all those Orlicz spaces which can be written as some Lorentz spaces. This description is an answer to the problem posed by Pustylnik in [E. Pustylnik, Ultrasymmetric spaces, J. London Math. Soc. (2) 68 (1) (2003) 165-182]. On the other hand, the Lorentz-Orlicz spaces with non-trivial indices of their fundamental functions are ultrasymmetric.

• 3.
Department of Mathematics and Mechanics, Samara State University, Department of Mathematics, Samara State University.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Rademacher functions in Morrey spaces2016In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 444, no 2, p. 1133-1154Article in journal (Refereed)

The Rademacher sums are investigated in the Morrey spaces Mp,wMp,w on [0,1][0,1] for 1≤p<∞1≤p<∞ and weight w being a quasi-concave function. They span l2l2 space in Mp,wMp,w if and only if the weight w is smaller than View the MathML sourcelog2−1/2⁡2t on (0,1)(0,1). Moreover, if 1<p<∞1<p<∞ the Rademacher subspace Rp,wRp,w is complemented in Mp,wMp,w if and only if it is isomorphic to l2l2. However, the Rademacher subspace R1,wR1,w is not complemented in M1,wM1,w for any quasi-concave weight w . In the last part of the paper geometric structure of Rademacher subspaces in Morrey spaces Mp,wMp,w is described. It turns out that for any infinite-dimensional subspace X of Rp,wRp,w the following alternative holds: either X is isomorphic to l2l2 or X contains a subspace which is isomorphic to c0c0 and is complemented in Rp,wRp,w.

• 4.
Luleå tekniska universitet.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. Departamento de Matemàtica, Aplicada i Anàlisi, Universitat de Barcelona.
Sharp weighted multidimensional integral inequalities of Chebyshev type1999In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 236, no 2, p. 243-253Article in journal (Refereed)

We prove a general Chebyshev inequality for monotone functions in higher dimensions. This result generalizes the classical one-dimensional inequality and recovers some extensions already known for product weights. In all cases we find the best constant in the inequality. We also consider the case of more general operators.

• 5.
Dipartimento di Fisica, Università di Roma “La Sapienza”, Rome.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
New evolution PDEs with many isochronous solutions2009In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 353, no 2, p. 481-488Article in journal (Refereed)

Certain nonlinear evolution PDEs in 1 + 1 variables (time and space) are identified, featuring a positive parameter ω and evolving, for a large class of initial data, periodically with the fixed period T = 2 π / ω (or perhaps over(T, ̃) = p T with p a small integer). They are autonomous (i.e., they do not feature any explicit dependence on the time variable), but they generally (although not quite all of them) depend explicitly on the space variable hence are not translation-invariant. They are integrable, having been obtained by applying an appropriate change of dependent and independent variables to certain nonlinear evolution PDEs whose integrable character has been recently ascertained. Solutions of some of these PDEs are exhibited.

• 6. Cheng, Yuanji
Hölder continuity of the inverse of p-Laplacian1998In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 221, no 2, p. 734-748Article in journal (Refereed)

In this note, we study the inverse operator (-Δp) - 1ofp-Lapalcian on a bounded domain Ω Rn. We show that (-Δp) - 1:W - 1, p′(Ω) → W1, p0(Ω) is Hölder continuous and is a compact operator fromV(q, s)toW1, p0(Ω), s (0, p′), q > p* the conjugate of critical Sobolev exponent. As an application, we study existence of positive solutions of two nonlinear elliptic equations

• 7.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Using a natural deconvolution for analysis of perturbed integer sampling in shift-invariant spaces2011In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 373, no 1, p. 271-286Article in journal (Refereed)

An important cornerstone of both wavelet and sampling theory is shift-invariant spaces, that is, spaces V spanned by a Riesz basis of integer-translates of a single function. Under some mild differentiability and decay assumptions on the Fourier transform of this function, we show that V also is generated by a function ϕ with Fourier transform equal to the convolution of g with the characteristic function living on the interval [-pi,pi]. We explain why analysis of this particular generating function can be more likely to provide large jitter bounds ε such that any f ∈ V can be reconstructed from perturbed integer samples f(k + ε_k) whenever the supremum of |ε_k| is smaller than ε. We use this natural deconvolution to further develop analysis techniques from a previous paper. Then we demonstrate the resulting analysis method on the class of spaces for which g has compact support and bounded variation (including all spaces generated by Meyer wavelet scaling functions), on some particular choices of ϕ for which we know of no previously published bounds and finally, we use it to improve some previously known bounds for B-spline shift-invariant spaces.

• 8.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Auto-hodograph transformations for a hierarchy of nonlinear evolution equations2001In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 257, no 1, p. 21-28Article in journal (Refereed)

We introduce nonlocal auto-hodograph transformations for a hierarchy of nonlinear evolution equations. This is accomplished by composing nonlocal transformations (one of which is a hodograph transformation) which linearize the given equations. This enables one to construct sequences of exact solutions for any equation belonging to the hierarchy.

• 9.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
School of Mathematical and Statistical Sciences, University of Natal, Durban.
First integrals and reduction of a class of nonlinear higher order ordinary differential equations2003In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 287, no 2, p. 473-486Article in journal (Refereed)

We propose a method for constructing first integrals of higher order ordinary differential equations. In particular third, fourth and fifth order equations of the form are considered. The relation of the proposed method to local and nonlocal symmetries are discussed.

• 10.
Luleå tekniska universitet.
Vanderbilt University, Department of Mathematics, Nashville.
Asynchronous exponential growth of semigroups of nonlinear operators1992In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 167, no 2, p. 443-467Article in journal (Refereed)

The property of asynchronous exponential growth is analyzed for the abstract nonlinear differential equation z′(t) = Az(t) + F(z(t)), t ≥ 0, z(0) = x ε{lunate} X, where A is the infinitesimal generator of a semigroup of linear operators in the Banach space X and F is a nonlinear operator in X. Asynchronous exponential growth means that the nonlinear semigroup S(t), t ≥ 0 associated with this problem has the property that there exists λ > 0 and a nonlinear operator Q in X such that the range of Q lies in a one-dimensional subspace of X and limt → ∞ e-λtS(t)x = Qx for all x ε{lunate} X. It is proved that if the linear semigroup generated by A has asynchronous exponential growth and F satisfies ∥F(x)∥ ≤ f(∥x∥) ∥x∥, where f: R+ → R+ and ∝∞( f(r) r) dr < ∞, then the nonlinear semigroup S(t), t ≥ 0 has asynchronous exponential growth. The method of proof is a linearization about infinity. Examples from structured population dynamics are given to illustrate the results

• 11.
Department of Mathematics, University of Delhi.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Remarks on recent results of Oguntuase and Imoru2001In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 255, no 1, p. 105-108Article in journal (Refereed)
• 12.
Kyushu Institute of Technology.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
On James and Jordan-von Neumann constants of Lorentz sequence spaces2001In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 258, no 2, p. 457-465Article in journal (Refereed)

The nonsquare or James constant $J(X)$ and the Jordan-von Neumann constant $C_{NJ}(X)$ are computed for two-dimensional Lorentz sequence spaces $d^{(2)}(w,q)$ in the case where $2\leq q<\infty$. The Jordan-von Neumann constant is also calculated in the case where $1\leq q<2$.

• 13.
Institute of Mathematics, Faculty of Electrical Engineering, Poznań University of Technology, Poznań, Poland.
Institute of Mathematics, Faculty of Electrical Engineering, Poznań University of Technology, Poznań, Poland. Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Symmetrization, factorization and arithmetic of quasi-Banach function spaces2019In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 470, no 2, p. 1136-1166Article in journal (Refereed)

We investigate relations between symmetrizations of quasi-Banach function spaces and constructions such as Calderón–Lozanovskiĭ spaces, pointwise product spaces and pointwise multipliers. We show that under reasonable assumptions the symmetrization commutates with these operations. We determine also the spaces of pointwise multipliers between Lorentz spaces and Cesàro spaces. The methods that we develop may be regarded as an arithmetic of quasi-Banach function spaces and proofs of Theorem 3, Theorem 4, Theorem 6 give a kind of tutorial for these methods. Finally, the above results will be used in proofs of some factorization results.

• 14. Koski, Timo
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. Department of Mathematics, University of Stockholm.
ε-entropy, ε-rate, and interpolation spaces revisited with an application to linear communication channels1994In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 186, no 1, p. 265-276Article in journal (Refereed)

Some results concerning the ϵ-rate and the ϵ-entropy presented by one of the authors (cf. [Peetre, Ricerche Mat. 17 (1968), pp. 216-220]) are investigated, updated, and generalized in various ways. In addition we give some examples, as well as a discussion, related to the problems presented by Hajela and Honig of this interpolation theory technique in an abstract model of digital communication.

• 15. Kruglyak, Natan
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Calderón-Lozanovski construction on weighted Banach function lattices2003In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 288, no 2, p. 744-757Article in journal (Refereed)

We show that the Calderón-Lozanovskiǐ construction (·) commute with arbitrary weighted Banach function lattices, that is, (E0(w0), E1 (w1)) = (E0, E1)(w) with w = 1/ (1/w0, 1/w1) if and only if is equivalent to a power function. From this result we can also get the Stein-Weiss theorem on interpolation of weighted Lp spaces and its generalizations

• 16.
Institute of Mathematics of Electric Faculty, Poznań University of Technology.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Abstract Cesàro spaces: Duality2015In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 424, no 2, p. 932-951Article in journal (Refereed)

We study abstract Cesàro spaces CX , which may be regarded as generalizations of Cesàro sequence spaces cespcesp and Cesàro function spaces Cesp(I)Cesp(I) on I=[0,1]I=[0,1] or I=[0,∞)I=[0,∞), and also as the description of optimal domain from which Cesàro operator acts to X . We find the dual of such spaces in a very general situation. What is however even more important, we do it in the simplest possible way. Our proofs are more elementary than the known ones for cespcesp and Cesp(I)Cesp(I). This is the point how our paper should be seen, i.e. not as a generalization of known results, but rather like grasping and exhibiting the general nature of the problem, which is not so easily visible in previous publications. Our results show also an interesting phenomenon that there is a big difference between duality in the cases of finite and infinite intervals.

• 17.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Department of Applied Mathematics, Chernivtsi National University. Institute of Mathematics, Cracow University of Technology.
On a problem of Eidelheit from The Scottish Book concerning absolutely continuous functions2011In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 375, no 2, p. 401-411Article in journal (Refereed)

A negative solution of Problem 188 posed by Max Eidelheit in the Scottish Book concerning superpositions of separately absolutely continuous functions is presented. We discuss here this and some related problems which have also negative solutions. Finally, we give an explanation of such negative answers from the "embeddings of Banach spaces" point of view.

• 18. Maligranda, Lech
Department of Mathematics, University of Zagreb. Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
On some inequalities of the Grüss-Barnes and Borell type1994In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 187, no 1, p. 306-323Article in journal (Refereed)

Some new generalizations of the Grüss-Barnes and Borell inequalities are proved. A new proof, using the classical Chebyshev inequality, for the case of two functions is presented and applied. A crucial inequality for $n$ functions by C. Borell \ref[J. Math. Anal. Appl. 41 (1973), 300--312; MR0315073 (47 \#3622)] is also discussed. Some recent results are sharpened and complemented. Interpolated or weighted versions of some of the inequalities are pointed out.

• 19. Maligranda, Lech
Faculty of Textile Technology, University of Zagreb. Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Weighted Favard and Berwald inequalities1995In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 190, no 1, p. 248-262Article in journal (Refereed)

Weighted versions of the Favard and Benwald inequalities are proved in the class of monotone and concave (convex) functions. Some necessary majorization estimates and a double-weight characterization for a Favard-type inequality are included.

• 20.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok. Department of Mathematics, Faculty of Science, Chiangmai University, Chiang Mai.
On the James constant and B-convexity of Cesàro and Cesàro–Orlicz sequence spaces2007In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 326, no 1, p. 312-331Article in journal (Refereed)

The classical James constant and the nth James constants, which are measure of B-convexity for the Cesàro sequence spaces cesp and the Cesàro–Orlicz sequence spaces cesM, are calculated. These investigations show that cesp, cesM are not uniformly non-square and even they are not B-convex. Therefore the classical Cesàro sequence spaces cesp are natural examples of reflexive spaces which are not B-convex. Moreover, the James constant for the two-dimensional Cesàro space ces₂(²) is calculated.

• 21.
Technical University of Civil Engineering Bucharest.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. Technical University of Civil Engineering Bucharest. University of Bucharest and Institute of Mathematics of Romanian Academy.
A new characterization of Bergman-Schatten spaces and a duality result2009In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 360, no 1, p. 67-80Article in journal (Refereed)

Let B0 (D, ℓ2) denote the space of all upper triangular matrices A such that limr → 1- (1 - r2) {norm of matrix} (A * C (r))′ {norm of matrix}B (ℓ2) = 0. We also denote by B0, c (D, ℓ2) the closed Banach subspace of B0 (D, ℓ2) consisting of all upper triangular matrices whose diagonals are compact operators. In this paper we give a duality result between B0, c (D, ℓ2) and the Bergman-Schatten spaces La1 (D, ℓ2). We also give a characterization of the more general Bergman-Schatten spaces Lap (D, ℓ2), 1 ≤ p < ∞, in terms of Taylor coefficients, which is similar to that of M. Mateljevic and M. Pavlovic [M. Mateljevic, M. Pavlovic, Lp-behaviour of the integral means of analytic functions, Studia Math. 77 (1984) 219-237] for classical Bergman spaces.

• 22. Oguntuase, James
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Refinement of Hardy's inequalities via superquadratic and subquadratic functions2008In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 339, no 2, p. 1305-1312Article in journal (Refereed)

A new refined weighted Hardy inequality for p ≥ 2 is proved and discussed. The inequality is reversed for 1 < p ≤ 2, which means that for p = 2 we have equality. The main tool in the proofs are some new results for superquadratic and subquadratic functions.

• 23. Oguntuase, James
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Multidimensional Hardy-type inequalities with general kernels2008In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 348, no 1, p. 411-418Article in journal (Refereed)

Some new multidimensional Hardy-type inequalities involving arithmetic mean operators with general positive kernels are derived. Our approach is mainly to use a convexity argument and the results obtained improve some known results in the literature and, in particular, some recent results in [S. Kaijser, L. Nikolova, L.-E. Persson, A. Wedestig, Hardy-type inequalities via convexity, Math. Inequal. Appl. 8 (3) (2005) 403-417] are generalized and complemented.

• 24. Okpoti, Christopher
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. Department of Mathematics, University of Western Ontario.
An equivalence theorem for some integral conditions with general measures related to Hardy's inequality2007In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 326, no 1, p. 398-413Article in journal (Refereed)

It is proved that, besides the usual Muckenhoupt condition, there exist four different scales of conditions for characterizing the Hardy type inequality with general measures for the case 1

• 25. Okpoti, Christopher
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. University of Western Ontario.
An equivalence theorem for some integral conditions with general measures related to Hardy's inequality II2008In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 337, no 1, p. 219-230Article in journal (Refereed)

Scales of equivalent weight characterizations for the Hardy type inequality with general measures are proved. The conditions are valid in the case of indices 01. We also include a reduction theorem for transferring a three-measure Hardy inequality to the case with two measures.

• 26.
Faculty of Textile Technology, University of Zagreb.
Faculty of Chemical Engineering, University of Zagreb. Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Integral inequalities for monotone functions1997In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 215, no 1, p. 235-251Article in journal (Refereed)

Some integral inequalities for generalized monotone functions of one variable and an integral inequality for monotone functions of several variables are proved. Some applications are presented and discussed.

• 27.
Faculty of Textile Technology, University of Zagreb.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
On Bergh's inequality for quasi-monotone functions1995In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 195, no 2, p. 393-400Article in journal (Refereed)

We consider an inverse Hölder type inequality of J. Bergh [Math Z.215 (1994), 205-208] yielding for quasi-concave functions. We prove that this inequality holds in a more general class of functions endowed with two quasimonotonicity growth conditions. Some classes of quasi-monotone functions in mean are introduced and some new Bergh-type inequalities in these classes are proved. Our proofs are short and completely different from that of J. Bergh.

• 28.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Weighted Hardy and potential operators in the generalized Morrey spaces2011In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 377, no 2, p. 792-806Article in journal (Refereed)

We study the weighted p→q-boundedness of the multi-dimensional Hardy type operators in the generalized Morrey spaces Lp,φ(Rn,w) defined by an almost increasing function φ(r) and radial type weight w(|x|). We obtain sufficient conditions, in terms of some integral inequalities imposed on φ and w, for such a p→q-boundedness. In some cases the obtained conditions are also necessary. These results are applied to derive a similar weighted p→q-boundedness of the Riesz potential operator

Integrability conditions on periodic functions related to their Fourier transforms1973In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 44, p. 291-309Article in journal (Refereed)
• 30.
Luleå tekniska universitet.
Review of developments in monitoring and control of mine ventilation systems1980In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, p. 223-229Article in journal (Refereed)

Increased use of diesel equipment underground in Sweden prompted visits to the U. S. , Canada and Europe to study the level of development of sensors for carbon monoxide, methane, air speed, pressure, temperature and moisture

• 31.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Exponentially growing solutions of parabolic Isaacs' equations2008In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 348, no 1, p. 337-345Article in journal (Refereed)

This paper contributes to the literature on unbounded viscosity solutions of fully nonlinear and possibly degenerate parabolic equations. Under natural assumptions, it is established that the initial-value problem for a degenerate parabolic Isaacs' equation set in (0, T] × R has a unique continuous viscosity solution with at most exponential growth at infinity.

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