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Persson, Lars-Erik

Open this publication in new window or tab >>A sharp boundedness result for restricted maximal operators of Vilenkin–Fourier series on martingale Hardy spaces### Blahota, I.

### Nagy, K.

### Persson, Lars-Erik

### Tephnadze, G.

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_0_j_idt195_some",{id:"formSmash:j_idt191:0:j_idt195:some",widgetVar:"widget_formSmash_j_idt191_0_j_idt195_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_0_j_idt195_otherAuthors",{id:"formSmash:j_idt191:0:j_idt195:otherAuthors",widgetVar:"widget_formSmash_j_idt191_0_j_idt195_otherAuthors",multiple:true}); 2019 (Estonian)In: Georgian Mathematical Journal, ISSN 1072-947X, E-ISSN 1572-9176, Vol. 26, no 3Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

Walter de Gruyter, 2019
##### Keywords

Vilenkin system, partial sums, maximal operator, Vilenkin–Fourier series, martingale Hardy space
##### National Category

Mathematical Analysis
##### Research subject

Mathematics
##### Identifiers

urn:nbn:se:ltu:diva-71225 (URN)10.1515/gmj-2018-0045 (DOI)000489300400004 ()
#####

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##### Note

Institute of Mathematics and Computer Sciences, College of Nyíregyháza, Nyíregyháza, Hungary.

Institute of Mathematics and Computer Sciences, College of Nyíregyháza, Nyíregyháza, Hungary.

Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. UiT the Arctic University of Norway, Narvik, Norway.

School of IT, Engineering and Mathematics, IV, University of Georgia, Tbilisi, Georgia.

The restricted maximal operators of partial sums with respect to bounded Vilenkin systems are investigated. We derive the maximal subspace of positive numbers, for which this operator is bounded from the Hardy space H p {H-{p}} to the Lebesgue space L p {L-{p}} for all 0 < p ≤ 1 {0<p\leq 1}. We also prove that the result is sharp in a particular sense.

Validerad;2019;Nivå 2;2019-10-09 (johcin)

Available from: 2018-10-16 Created: 2018-10-16 Last updated: 2019-10-28Bibliographically approvedOpen this publication in new window or tab >>A new generalization of Boas theorem for some Lorentz spaces lambda(q)(omega)### Kopezhanova, Aigerim

### Nursultanov, Erlan

### Persson, Lars-Erik

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_1_j_idt195_some",{id:"formSmash:j_idt191:1:j_idt195:some",widgetVar:"widget_formSmash_j_idt191_1_j_idt195_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_1_j_idt195_otherAuthors",{id:"formSmash:j_idt191:1:j_idt195:otherAuthors",widgetVar:"widget_formSmash_j_idt191_1_j_idt195_otherAuthors",multiple:true}); 2018 (English)In: Journal of Mathematical Inequalities, ISSN 1846-579X, E-ISSN 1848-9575, Vol. 12, no 3, p. 619-633Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

Element, 2018
##### National Category

Mathematical Analysis
##### Research subject

Mathematics
##### Identifiers

urn:nbn:se:ltu:diva-71213 (URN)10.7153/jmi-2018-12-47 (DOI)000445366500002 ()2-s2.0-85063225498 (Scopus ID)
#####

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#####

##### Note

Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. LN Gumilyov Eurasian Natl Univ, Fac Mech & Math, Astana, Kazakhstan.

RUDN Univ, Moscow, Russia. Lomonosov Moscow State Univ, Kazakhstan Branch, Astana, Kazakhstan.

Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. Artic Univ Norway, UiT, Narvik, Norway.

Let Lambda(q)(omega), q > 0, denote the Lorentz space equipped with the (quasi) norm parallel to f parallel to(Lambda q(omega)) := (integral(1)(0) (f*(t)omega(t))(q)dt/t)(1/q) for a function integral on [0,1] and with omega positive and equipped with some additional growth properties. A generalization of Boas theorem in the form of a two-sided inequality is obtained in the case of both general regular system Phi = {phi(k)}(k=1)(infinity) and generalized Lorentz Lambda(q) (omega) spaces.

Validerad;2018;Nivå 2;2018-10-15 (johcin)

Available from: 2018-10-15 Created: 2018-10-15 Last updated: 2019-04-01Bibliographically approvedOpen this publication in new window or tab >>Convex Functions and Their Applications: A Contemporary Approach### Niculescu, Constantin P.

### Persson, Lars-Erik

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_2_j_idt195_some",{id:"formSmash:j_idt191:2:j_idt195:some",widgetVar:"widget_formSmash_j_idt191_2_j_idt195_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_2_j_idt195_otherAuthors",{id:"formSmash:j_idt191:2:j_idt195:otherAuthors",widgetVar:"widget_formSmash_j_idt191_2_j_idt195_otherAuthors",multiple:true}); 2018 (English)Book (Refereed)
##### Abstract [en]

##### Place, publisher, year, edition, pages

Cham: Springer, 2018. p. 415
##### Series

CMS Books in Mathematics, ISSN 1613-5237
##### National Category

Mathematical Analysis
##### Research subject

Mathematics
##### Identifiers

urn:nbn:se:ltu:diva-69635 (URN)10.1007/978-3-319-78337-6 (DOI)978-3-319-78336-9 (ISBN)978-3-319-78337-6 (ISBN)
#####

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Available from: 2018-06-18 Created: 2018-06-18 Last updated: 2018-06-18Bibliographically approved

Department of Mathematics, University of Craiova .

Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. UiT, The Artic University of Norway, Campus Narvik .

This second edition provides a thorough introduction to contemporary convex function theory with many new results. A large variety of subjects are covered, from the one real variable case to some of the most advanced topics. The new edition includes considerably more material emphasizing the rich applicability of convex analysis to concrete examples. Chapters 4, 5, and 6 are entirely new, covering important topics such as the Hardy-Littlewood-Pólya-Schur theory of majorization, matrix convexity, and the Legendre-Fenchel-Moreau duality theory.

This book can serve as a reference and source of inspiration to researchers in several branches of mathematics and engineering, and it can also be used as a reference text for graduate courses on convex functions and applications.

Open this publication in new window or tab >>Convex Functions on a Normed Linear Space### Niculescu, Constantin P.

### Persson, Lars-Erik

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_3_j_idt195_some",{id:"formSmash:j_idt191:3:j_idt195:some",widgetVar:"widget_formSmash_j_idt191_3_j_idt195_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_3_j_idt195_otherAuthors",{id:"formSmash:j_idt191:3:j_idt195:otherAuthors",widgetVar:"widget_formSmash_j_idt191_3_j_idt195_otherAuthors",multiple:true}); 2018 (English)In: Duality and Convex Optimization, Cham: Springer, 2018, p. 107-184Chapter in book (Refereed)
##### Abstract [en]

##### Place, publisher, year, edition, pages

Cham: Springer, 2018
##### Series

CMS Books in Mathematics, ISSN 1613-5237
##### National Category

Mathematical Analysis
##### Research subject

Mathematics
##### Identifiers

urn:nbn:se:ltu:diva-69632 (URN)10.1007/978-3-319-78337-6_3 (DOI)978-3-319-78336-9 (ISBN)978-3-319-78337-6 (ISBN)
#####

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Available from: 2018-06-18 Created: 2018-06-18 Last updated: 2018-06-18Bibliographically approved

Department of Mathematics, University of Craiova .

Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. UiT, The Artic University of Norway, Campus Narvik .

Convex functions and their relatives are ubiquitous in a large variety of applications such as optimization theory, mass transportation, mathematical economics, and geometric inequalities related to isoperimetric problems. This chapter is devoted to a succinct presentation of their theory in the context of *real* normed linear spaces, but most of the illustrations will refer to the Euclidean space RN,">RN,RN, the matrix space MN(R)">MN(R)MN(R) of all N×N">N×NN×N-dimensional real matrices (endowed with the Hilbert–Schmidt norm or with the operator norm), and the Lebesgue spaces Lp(RN)">Lp(RN)Lp(RN) with p∈[1,∞]">p∈[1,∞]p∈[1,∞].

Open this publication in new window or tab >>Convex Functions on Intervals### Niculescu, Constantin P.

### Persson, Lars-Erik

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_4_j_idt195_some",{id:"formSmash:j_idt191:4:j_idt195:some",widgetVar:"widget_formSmash_j_idt191_4_j_idt195_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_4_j_idt195_otherAuthors",{id:"formSmash:j_idt191:4:j_idt195:otherAuthors",widgetVar:"widget_formSmash_j_idt191_4_j_idt195_otherAuthors",multiple:true}); 2018 (English)In: Duality and Convex Optimization, Cham: Springer, 2018, p. 1-70Chapter in book (Refereed)
##### Abstract [en]

##### Place, publisher, year, edition, pages

Cham: Springer, 2018
##### Series

CMS Books in Mathematics, ISSN 1613-5237
##### National Category

Mathematical Analysis
##### Research subject

Mathematics
##### Identifiers

urn:nbn:se:ltu:diva-69631 (URN)10.1007/978-3-319-78337-6_1 (DOI)978-3-319-78336-9 (ISBN)978-3-319-78337-6 (ISBN)
#####

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Available from: 2018-06-18 Created: 2018-06-18 Last updated: 2019-01-16Bibliographically approved

Department of Mathematics, University of Craiova .

Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. UiT, The Artic University of Norway, Campus Narvik .

The study of convex functions of one real variable offers an excellent glimpse of the beauty and fascination of advanced mathematics. The reader will find here a large variety of results based on simple and intuitive arguments that have remarkable applications. At the same time they provide the starting point of deep generalizations in the setting of several variables, that will be discussed in the next chapters.

Open this publication in new window or tab >>Convex Sets in Real Linear Spaces### Niculescu, Constantin P.

### Persson, Lars-Erik

Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. UiT, The Artic University of Norway, Campus Narvik .PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_5_j_idt195_some",{id:"formSmash:j_idt191:5:j_idt195:some",widgetVar:"widget_formSmash_j_idt191_5_j_idt195_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_5_j_idt195_otherAuthors",{id:"formSmash:j_idt191:5:j_idt195:otherAuthors",widgetVar:"widget_formSmash_j_idt191_5_j_idt195_otherAuthors",multiple:true}); 2018 (English)In: Convex Functions and Their Applications: A Contemporary Approach, Cham: Springer, 2018, p. 71-106Chapter in book (Refereed)
##### Abstract [en]

##### Place, publisher, year, edition, pages

Cham: Springer, 2018
##### Series

CMS Books in Mathematics, ISSN 1613-5237
##### National Category

Mathematical Analysis
##### Research subject

Mathematics
##### Identifiers

urn:nbn:se:ltu:diva-69578 (URN)10.1007/978-3-319-78337-6_2 (DOI)978-3-319-78336-9 (ISBN)978-3-319-78337-6 (ISBN)
#####

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Available from: 2018-06-15 Created: 2018-06-15 Last updated: 2018-06-15Bibliographically approved

Department of Mathematics, University of Craiova .

The natural domain for a convex function is a convex set. In this chapter we review some basic facts, necessary for a deep understanding of the concept of convexity in real linear spaces. For reader’s convenience, all results concerning the separation of convex sets in Banach spaces are stated in Section 2.2 with proofs covering only the particular (but important) case of Euclidean spaces. Full details in the general case are to be found in Appendix B

Open this publication in new window or tab >>Convexity and Majorization### Niculescu, Constantin P.

### Persson, Lars-Erik

Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. UiT, The Artic University of Norway, Campus Narvik .PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_6_j_idt195_some",{id:"formSmash:j_idt191:6:j_idt195:some",widgetVar:"widget_formSmash_j_idt191_6_j_idt195_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_6_j_idt195_otherAuthors",{id:"formSmash:j_idt191:6:j_idt195:otherAuthors",widgetVar:"widget_formSmash_j_idt191_6_j_idt195_otherAuthors",multiple:true}); 2018 (English)In: Convex Functions and Their Applications: A Contemporary Approach, Cham: Springer, 2018, p. 185-226Chapter in book (Refereed)
##### Abstract [en]

##### Place, publisher, year, edition, pages

Cham: Springer, 2018
##### Series

CMS Books in Mathematics, ISSN 1613-5237
##### National Category

Mathematical Analysis
##### Research subject

Mathematics
##### Identifiers

urn:nbn:se:ltu:diva-69580 (URN)10.1007/978-3-319-78337-6_4 (DOI)978-3-319-78336-9 (ISBN)978-3-319-78337-6 (ISBN)
#####

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Available from: 2018-06-15 Created: 2018-06-15 Last updated: 2018-06-15Bibliographically approved

Department of Mathematics, University of Craiova .

This chapter is aimed to offer a glimpse on the majorization theory and the beautiful inequalities associated to it. Introduced by G. H. Hardy, J. E. Littlewood, and G. Pólya (Messenger Math. 58:145–152, (1929), [208]) in 1929, and popularized by their celebrated book on *Inequalities* (Hardy et al., Inequalities, Cambridge University Press, 1952, [209]), the relation of majorization has attracted along the time a big deal of attention not only from the mathematicians, but also from people working in various other fields such as statistics, economics, physics, signal processing, data mining, etc. Part of this research activity is summarized in the 900 pages of the recent book by A. W. Marshall, I. Olkin, and B. Arnold (Inequalities: theory of majorization and its applications. Springer, New York (2011), [305]).

Open this publication in new window or tab >>Convexity in Spaces of Matrices### Niculescu, Constantin P.

### Persson, Lars-Erik

Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. UiT, The Artic University of Norway, Campus Narvik .PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_7_j_idt195_some",{id:"formSmash:j_idt191:7:j_idt195:some",widgetVar:"widget_formSmash_j_idt191_7_j_idt195_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_7_j_idt195_otherAuthors",{id:"formSmash:j_idt191:7:j_idt195:otherAuthors",widgetVar:"widget_formSmash_j_idt191_7_j_idt195_otherAuthors",multiple:true}); 2018 (English)In: Convex Functions and Their Applications: A Contemporary Approach, Cham: Springer, 2018, p. 227-254Chapter in book (Refereed)
##### Abstract [en]

##### Place, publisher, year, edition, pages

Cham: Springer, 2018
##### Series

CMS Books in Mathematics, ISSN 1613-5237
##### National Category

Mathematical Analysis
##### Research subject

Mathematics
##### Identifiers

urn:nbn:se:ltu:diva-69633 (URN)10.1007/978-3-319-78337-6_5 (DOI)978-3-319-78336-9 (ISBN)978-3-319-78337-6 (ISBN)
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Available from: 2018-06-18 Created: 2018-06-18 Last updated: 2020-03-05Bibliographically approved

Department of Mathematics, University of Craiova .

In this chapter we investigate three subjects concerning the convexity of functions defined on a space of matrices (or just on a convex subset of it). The first one is devoted to the convex spectral functions, that is, to the convex functions F:Sym(n,R)→R">F:Sym(n,R)→RF:Sym(n,R)→R whose values *F*(*A*) depend only on the spectrum of *A*. The main result concerns their description as superpositions f∘Λ">f∘Λf∘Λ between convex functions f:Rn→R">f:Rn→Rf:Rn→R invariant under permutations, and the eigenvalues map Λ">ΛΛ.

Open this publication in new window or tab >>Duality and Convex Optimization### Niculescu, Constantin P.

### Persson, Lars-Erik

Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. UiT, The Artic University of Norway, Campus Narvik .PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_8_j_idt195_some",{id:"formSmash:j_idt191:8:j_idt195:some",widgetVar:"widget_formSmash_j_idt191_8_j_idt195_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_8_j_idt195_otherAuthors",{id:"formSmash:j_idt191:8:j_idt195:otherAuthors",widgetVar:"widget_formSmash_j_idt191_8_j_idt195_otherAuthors",multiple:true}); 2018 (English)In: Convex Functions and Their Applications: A Contemporary Approach, Cham: Springer, 2018, p. 255-300Chapter in book (Refereed)
##### Abstract [en]

##### Place, publisher, year, edition, pages

Cham: Springer, 2018
##### Series

CMS Books in Mathematics, ISSN 1613-5237
##### National Category

Mathematical Analysis
##### Research subject

Mathematics
##### Identifiers

urn:nbn:se:ltu:diva-69630 (URN)10.1007/978-3-319-78337-6_6 (DOI)978-3-319-78336-9 (ISBN)978-3-319-78337-6 (ISBN)
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Available from: 2018-06-18 Created: 2018-06-18 Last updated: 2020-03-05Bibliographically approved

Department of Mathematics, University of Craiova .

Convex optimization is one of the main applications of the theory of convexity and Legendre–Fenchel duality is a basic tool, making more flexible the approach of many concrete problems. The diet problem, the transportation problem, and the optimal assignment problem are among the many problems that during the Second World War and immediately after led L. Kantorovich, T. C. Koopmans, F. L. Hitchcock, and G. B. Danzig to develop the mathematical theory of linear programming. Soon it was realized that most results extend to the framework of convex functions, which marked the birth of convex programming. Later on, W. Fenchel, R. T. Rockafellar, and J. J. Moreau laid the foundations of convex analysis.

Open this publication in new window or tab >>Extensions and Refinements of Fejer and Hermite–Hadamard Type Inequalities### Abramovich, S.

### Persson, Lars-Erik

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_9_j_idt195_some",{id:"formSmash:j_idt191:9:j_idt195:some",widgetVar:"widget_formSmash_j_idt191_9_j_idt195_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_9_j_idt195_otherAuthors",{id:"formSmash:j_idt191:9:j_idt195:otherAuthors",widgetVar:"widget_formSmash_j_idt191_9_j_idt195_otherAuthors",multiple:true}); 2018 (English)In: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 21, no 3, p. 759-772Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

Element, 2018
##### National Category

Mathematical Analysis
##### Research subject

Mathematics
##### Identifiers

urn:nbn:se:ltu:diva-70848 (URN)10.7153/mia-2018-21-54 (DOI)000444628200011 ()2-s2.0-85052715296 (Scopus ID)
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##### Note

Department of Mathematics, University of Haifa, Haifa, Israel.

Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. UIT The Arctic University of Norway, Narvik, Norway.

In this paper extensions and refinements of Hermite-Hadamard and Fejer type inequalities are derived including monotonicity of some functions related to the Fejer inequality and extensions for functions, which are 1-quasiconvex and for function with bounded second derivative. We deal also with Fejer inequalities in cases that p, the weight function in Fejer inequality, is not symmetric but monotone on [a, b] .

Validerad;2018;Nivå 2;2018-09-12 (svasva)

Available from: 2018-09-12 Created: 2018-09-12 Last updated: 2018-10-10Bibliographically approved