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Kruglyak, Natan
Publications (10 of 23) Show all publications
Asekritova, I. & Kruglyak, N. (2008). Invertibility of operators in spaces of real interpolation (ed.). Revista Matematica Complutense, 21(1), 207-217
Open this publication in new window or tab >>Invertibility of operators in spaces of real interpolation
2008 (English)In: Revista Matematica Complutense, ISSN 1139-1138, Vol. 21, no 1, p. 207-217Article in journal (Refereed) Published
Abstract [en]

Let A be a linear bounded operator from a couple X→ = (X0, X1) to a couple Y→ = (Y0, Y1) such that the restrictions of A on the spaces X0 and X1 have bounded inverses. This condition does not imply that the restriction of A on the real interpolation space (X0, X 1)θ, q has a bounded inverse for all values of the parameters θ and q. In this paper under some conditions on the kernel of A we describe all spaces (X0, X1)θ,q such that the operator A : (x0,X1)θ,q → (Y0, Y1) has a bounded inverse

National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
urn:nbn:se:ltu:diva-10804 (URN)9ab41920-8676-11dd-8275-000ea68e967b (Local ID)9ab41920-8676-11dd-8275-000ea68e967b (Archive number)9ab41920-8676-11dd-8275-000ea68e967b (OAI)
Note

Godkänd; 2008; 20080919 (ysko)

Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-02-27Bibliographically approved
Kruglyak, N. & Setterqvist, E. (2008). Sharp estimates for the identity minus Hardy operator on the cone of decreasing functions (ed.). Proceedings of the American Mathematical Society, 136(7), 2505-2513
Open this publication in new window or tab >>Sharp estimates for the identity minus Hardy operator on the cone of decreasing functions
2008 (English)In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 136, no 7, p. 2505-2513Article in journal (Refereed) Published
Abstract [en]

It is shown that if we restrict the identity minus Hardy operator on the cone of nonnegative decreasing functions f in L-p, then we have the sharp estimate parallel to(I - H)f parallel to(Lp) <= 1/(p - 1)(1/p) parallel to f parallel to(Lp) for p = 2, 3, 4, .... In other words,parallel to f** - f*parallel to(Lp) <= 1/(p - 1)(1/p) parallel to f parallel to(Lp) for each f is an element of L-p and each integer p >= 2.It is also shown, via a connection between the operator I - H and Laguerre functions, thatparallel to(1 - alpha)I + Phi(I - H)parallel to(L2 -> L2) = parallel to I - alpha H parallel to(L2 -> L2) = 1 for all a is an element of [ 0, 1].

National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
urn:nbn:se:ltu:diva-8914 (URN)10.1090/S0002-9939-08-09200-9 (DOI)000254675200029 ()2-s2.0-77950803201 (Scopus ID)776ed380-6c44-11dc-89fb-000ea68e967b (Local ID)776ed380-6c44-11dc-89fb-000ea68e967b (Archive number)776ed380-6c44-11dc-89fb-000ea68e967b (OAI)
Note

Validerad; 2008; 20070926 (natan)

Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-07-10Bibliographically approved
Kruglyak, N. (2007). The K-functional and Calderón-Zygmund type decompositions (ed.). In: (Ed.), Laura De Carli; Mario Milman (Ed.), Interpolation theory and applications: Proceedings of the Conference on Interpolation Theory and Applications in honor of Professor Michael Cwikel (Miami, FL, 2006). Paper presented at Conference on Interpolation Theory and Applications in honor of Professor Michael Cwikel : 01/04/2006 - 02/04/2006 (pp. 183-194). American Mathematical Society (AMS)
Open this publication in new window or tab >>The K-functional and Calderón-Zygmund type decompositions
2007 (English)In: Interpolation theory and applications: Proceedings of the Conference on Interpolation Theory and Applications in honor of Professor Michael Cwikel (Miami, FL, 2006) / [ed] Laura De Carli; Mario Milman, American Mathematical Society (AMS), 2007, p. 183-194Conference paper, Published paper (Refereed)
Place, publisher, year, edition, pages
American Mathematical Society (AMS), 2007
Series
Contemporary Mathematics ; 445
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
urn:nbn:se:ltu:diva-39143 (URN)dc5ee510-e452-11dc-b4b0-000ea68e967b (Local ID)978-0-8218-4207-2 (ISBN)dc5ee510-e452-11dc-b4b0-000ea68e967b (Archive number)dc5ee510-e452-11dc-b4b0-000ea68e967b (OAI)
Conference
Conference on Interpolation Theory and Applications in honor of Professor Michael Cwikel : 01/04/2006 - 02/04/2006
Note

Validerad; 2007; 20080226 (ysko)

Available from: 2016-10-03 Created: 2016-10-03 Last updated: 2018-02-27Bibliographically approved
Kruglyak, N. & Kuznetsov, E. (2007). The limiting case of the Marcinkiewicz integral: growth for convex sets (ed.). Proceedings of the American Mathematical Society, 135(10), 3283-3293
Open this publication in new window or tab >>The limiting case of the Marcinkiewicz integral: growth for convex sets
2007 (English)In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 135, no 10, p. 3283-3293Article in journal (Refereed) Published
Abstract [en]

The Marcinkiewicz integral Iλ (x)= ∫ (dist (y, ℝn\Ω))λ/Ω| x - y | n+λ dy, where λ > 0, plays a well-known and prominent role in harmonic analysis. In this paper, we estimate the growth of it in the limiting case λ → 0. Throughout, we assume that Ω is convex; it is interesting that this condition cannot be dropped

National Category
Mathematical Analysis Tribology (Interacting Surfaces including Friction, Lubrication and Wear)
Research subject
Mathematics; Machine Elements
Identifiers
urn:nbn:se:ltu:diva-11840 (URN)10.1090/S0002-9939-07-08856-9 (DOI)000248207600030 ()2-s2.0-77950829102 (Scopus ID)add8afa0-6c43-11dc-89fb-000ea68e967b (Local ID)add8afa0-6c43-11dc-89fb-000ea68e967b (Archive number)add8afa0-6c43-11dc-89fb-000ea68e967b (OAI)
Note

Validerad; 2007; 20070926 (natan)

Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-07-10Bibliographically approved
Kruglyak, N. (2006). An elementary proof of the real version of the Riesz-Thorin theorem (ed.). In: (Ed.), Interpolation theory and applications: [Proceedings of the Conference on Interpolation Theory and Applications in honor of Professor Michael Cwikel (Miami, FL, 2006)]. Paper presented at Conference on Interpolation Theory and Applications in honor of Professor Michael Cwikel : 01/04/2006 - 02/04/2006 (pp. 179-182). American Mathematical Society (AMS)
Open this publication in new window or tab >>An elementary proof of the real version of the Riesz-Thorin theorem
2006 (English)In: Interpolation theory and applications: [Proceedings of the Conference on Interpolation Theory and Applications in honor of Professor Michael Cwikel (Miami, FL, 2006)], American Mathematical Society (AMS), 2006, p. 179-182Conference paper, Published paper (Refereed)
Place, publisher, year, edition, pages
American Mathematical Society (AMS), 2006
Series
Contemporary Mathematics, ISSN 1098-3627 ; 445
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
urn:nbn:se:ltu:diva-31105 (URN)52acff40-e453-11dc-b4b0-000ea68e967b (Local ID)978-0-8218-4207-2 (ISBN)52acff40-e453-11dc-b4b0-000ea68e967b (Archive number)52acff40-e453-11dc-b4b0-000ea68e967b (OAI)
Conference
Conference on Interpolation Theory and Applications in honor of Professor Michael Cwikel : 01/04/2006 - 02/04/2006
Note

Validerad; 2006; 20080226 (ysko)

Available from: 2016-09-30 Created: 2016-09-30 Last updated: 2018-02-27Bibliographically approved
Kruglyak, N. (2006). Calderón-Zygmund type decompositions and applications (ed.). Proceedings of the Estonian Academy of Sciences: Physics, Mathematics, 55(3), 170-173
Open this publication in new window or tab >>Calderón-Zygmund type decompositions and applications
2006 (English)In: Proceedings of the Estonian Academy of Sciences: Physics, Mathematics, ISSN 1406-0086, E-ISSN 2228-0685, Vol. 55, no 3, p. 170-173Article in journal (Refereed) Published
Abstract [en]

In the paper a variant of the abstract approach to the Calderón-Zygmund type decompositions is considered. Applications to K-closedness of spaces of analytic functions are given.

National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
urn:nbn:se:ltu:diva-15602 (URN)f238a050-c357-11db-9ea3-000ea68e967b (Local ID)f238a050-c357-11db-9ea3-000ea68e967b (Archive number)f238a050-c357-11db-9ea3-000ea68e967b (OAI)
Note

Validerad; 2006; 20070115 (kani)

Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-02-27Bibliographically approved
Asekritova, I. & Kruglyak, N. (2006). Interpolation of Besov and Sobolev Spaces in the non-diagonal case (ed.). In: (Ed.), R. Bojanov (Ed.), Constructive Theory of Functions: Proceedings of International Conference, Varna. Paper presented at International Conference on Constructive Theory of Functions : 01/06/2005 - 07/06/2005 (pp. 45-50). Sofia: Prof. Marin Drinov Academic Publishing House
Open this publication in new window or tab >>Interpolation of Besov and Sobolev Spaces in the non-diagonal case
2006 (English)In: Constructive Theory of Functions: Proceedings of International Conference, Varna / [ed] R. Bojanov, Sofia: Prof. Marin Drinov Academic Publishing House, 2006, p. 45-50Conference paper, Published paper (Refereed)
Place, publisher, year, edition, pages
Sofia: Prof. Marin Drinov Academic Publishing House, 2006
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
urn:nbn:se:ltu:diva-30174 (URN)3e939680-25aa-11dc-b6d3-000ea68e967b (Local ID)954-322-144-8 (ISBN)3e939680-25aa-11dc-b6d3-000ea68e967b (Archive number)3e939680-25aa-11dc-b6d3-000ea68e967b (OAI)
Conference
International Conference on Constructive Theory of Functions : 01/06/2005 - 07/06/2005
Note

Godkänd; 2006; 20070628 (ysko)

Available from: 2016-09-30 Created: 2016-09-30 Last updated: 2018-02-27Bibliographically approved
Asekritova, I. & Kruglyak, N. (2006). Interpolation of Besov spaces in the nondiagonal case (ed.). St. Petersburg Mathematical Journal, 18(4), 1-9
Open this publication in new window or tab >>Interpolation of Besov spaces in the nondiagonal case
2006 (Russian)In: St. Petersburg Mathematical Journal, ISSN 1061-0022, E-ISSN 1547-7371, Vol. 18, no 4, p. 1-9Article in journal (Refereed) Published
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
urn:nbn:se:ltu:diva-7174 (URN)10.1090/S1061-0022-07-00958-2 (DOI)2-s2.0-85009797024 (Scopus ID)57f7c7c0-a573-11db-9811-000ea68e967b (Local ID)57f7c7c0-a573-11db-9811-000ea68e967b (Archive number)57f7c7c0-a573-11db-9811-000ea68e967b (OAI)
Note

Godkänd; 2006; Bibliografisk uppgift: Translated in St. Petersburg Math. J. Vol. 18 (2007), No. 4, Pages 511–516 S 1061-0022(07)00958-2; 20070115 (kani)

Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-07-10Bibliographically approved
Kruglyak, N. & Kuznetsov, E. (2006). Sharp integral estimates for the fractional maximal function and interpolation (ed.). Arkiv för matematik, 44(2), 309-326
Open this publication in new window or tab >>Sharp integral estimates for the fractional maximal function and interpolation
2006 (English)In: Arkiv för matematik, ISSN 0004-2080, E-ISSN 1871-2487, Vol. 44, no 2, p. 309-326Article in journal (Refereed) Published
Abstract [en]

We give sharp estimates for the fractional maximal function in terms of Hausdorff capacity. At the same time we identify the real interpolation spaces between L 1 and the Morrey space L 1,λ . The result can be viewed as an analogue of the Hardy-Littlewood maximal theorem for the fractional maximal function.

National Category
Tribology (Interacting Surfaces including Friction, Lubrication and Wear) Mathematical Analysis
Research subject
Machine Elements; Mathematics
Identifiers
urn:nbn:se:ltu:diva-10435 (URN)10.1007/s11512-006-0019-4 (DOI)000244917300007 ()2-s2.0-34147220617 (Scopus ID)93d40b50-09ff-11dc-9854-000ea68e967b (Local ID)93d40b50-09ff-11dc-9854-000ea68e967b (Archive number)93d40b50-09ff-11dc-9854-000ea68e967b (OAI)
Note

Validerad; 2006; 20070524 (ysko)

Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-07-10Bibliographically approved
Kislyakov, S. V. & Kruglyak, N. (2006). Stability of approximation under the action of singular integral operators (ed.). Functional analysis and its applications, 40(4), 285-297
Open this publication in new window or tab >>Stability of approximation under the action of singular integral operators
2006 (English)In: Functional analysis and its applications, ISSN 0016-2663, E-ISSN 1573-8485, Vol. 40, no 4, p. 285-297Article in journal (Refereed) Published
Abstract [en]

Let T be a singular integral operator, and let 0 < α < 1. If t > 0 and the functions f and Tf are both integrable, then there exists a function g ε BLipα(ct)) such that ∥f - g∥≤ Cdist L1 (f, BLipα (t)and ∥Tf-Tg ∥ L 1 ≤ c ∥ f-g ∥ L1 +dist L1 (Tf B Lip α(t)). (Here B X (τ) is the ball of radius τ and centered at zero in the space X; the constants C and c do not depend on t and f.) The function g is independent of T and is constructed starting with f by a nearly algorithmic procedure resembling the classical Calderón-Zygmund decomposition.

National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
urn:nbn:se:ltu:diva-4162 (URN)10.1007/s10688-006-0045-9 (DOI)000243542200004 ()2-s2.0-33846163760 (Scopus ID)20e384e0-62b0-11dc-ac97-000ea68e967b (Local ID)20e384e0-62b0-11dc-ac97-000ea68e967b (Archive number)20e384e0-62b0-11dc-ac97-000ea68e967b (OAI)
Note

Validerad; 2006; 20070914 (pirkko)

Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-07-10Bibliographically approved
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