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Publications (10 of 24) Show all publications
Kolyada, V. (2019). On the Cèsaro and Copson Norms of Nonnegative Sequences. Ukrainian Mathematical Journal, 71(2), 248-258
Open this publication in new window or tab >>On the Cèsaro and Copson Norms of Nonnegative Sequences
2019 (English)In: Ukrainian Mathematical Journal, ISSN 0041-5995, E-ISSN 1573-9376, Vol. 71, no 2, p. 248-258Article in journal (Refereed) Published
Abstract [en]

The Cèsaro and Copson norms of a nonnegative sequence are the lp -norms of its arithmetic means and the corresponding conjugate means. It is well known that, for 1 < p < 1, these norms are equivalent. In 1996, G. Bennett posed the problem of finding the best constants in the associated inequalities. The solution of this problem requires the evaluation of four constants. Two of them were found by Bennett. We find one of the two unknown constants and also prove one optimal weighted-type estimate for the remaining constant.

Place, publisher, year, edition, pages
Springer, 2019
National Category
Mathematics
Research subject
Mathematics
Identifiers
urn:nbn:se:kau:diva-75741 (URN)10.1007/s11253-019-01642-7 (DOI)000509896300008 ()2-s2.0-85073948250 (Scopus ID)
Available from: 2019-11-12 Created: 2019-11-12 Last updated: 2020-02-20Bibliographically approved
Kolyada, V. & Soria, J. (2016). Mixed Norms and Iterated Rearrangements. Zeitschrift für Analysis und ihre Anwendungen, 35(2), 119-138
Open this publication in new window or tab >>Mixed Norms and Iterated Rearrangements
2016 (English)In: Zeitschrift für Analysis und ihre Anwendungen, ISSN 0232-2064, E-ISSN 1661-4534, Vol. 35, no 2, p. 119-138Article in journal (Refereed) Published
Abstract [en]

We prove sharp estimates, and find the optimal range of indices, for the comparison of mixed norms for both functions and their iterated rearrangements.

Place, publisher, year, edition, pages
EUROPEAN MATHEMATICAL SOC, 2016
Keywords
Rearrangements, embeddings, mixed norms, Lorentz spaces
National Category
Mathematics
Research subject
Mathematics
Identifiers
urn:nbn:se:kau:diva-54916 (URN)10.4171/ZAA/1557 (DOI)000388453600001 ()
Available from: 2017-06-08 Created: 2017-06-08 Last updated: 2019-12-02Bibliographically approved
Kolyada, V. & Perez Lazaro, F. J. (2014). On Gagliardo-Nirenberg Type Inequalities. Journal of Fourier Analysis and Applications, 20(3), 577-607
Open this publication in new window or tab >>On Gagliardo-Nirenberg Type Inequalities
2014 (English)In: Journal of Fourier Analysis and Applications, ISSN 1069-5869, E-ISSN 1531-5851, Vol. 20, no 3, p. 577-607Article in journal (Refereed) Published
Abstract [en]

We present a Gagliardo-Nirenberg inequality which bounds Lorentz norms of a function by Sobolev norms and homogeneous Besov quasinorms with negative smoothness. We prove also other versions involving Besov or Triebel-Lizorkin quasinorms. These inequalities can be considered as refinements of Sobolev type embeddings. They can also be applied to obtain Gagliardo-Nirenberg inequalities in some limiting cases. Our methods are based on estimates of rearrangements in terms of heat kernels. These methods enable us to cover also the case of Sobolev norms with p = 1.

Place, publisher, year, edition, pages
Springer, 2014
Keywords
Gagliardo-Nirenberg inequality, Sobolev spaces, Besov spaces, Triebel-Lizorkin spaces
National Category
Mathematics
Identifiers
urn:nbn:se:kau:diva-41523 (URN)10.1007/s00041-014-9320-y (DOI)000337789300007 ()
Available from: 2016-04-25 Created: 2016-04-11 Last updated: 2017-11-30Bibliographically approved
Kolyada, V. (2014). Optimal relationships between L-p-norms for the Hardy operator and its dual. Annali di Matematica Pura ed Applicata, 193(2), 423-430
Open this publication in new window or tab >>Optimal relationships between L-p-norms for the Hardy operator and its dual
2014 (English)In: Annali di Matematica Pura ed Applicata, ISSN 0373-3114, E-ISSN 1618-1891, Vol. 193, no 2, p. 423-430Article in journal (Refereed) Published
Abstract [en]

We obtain sharp two-sided inequalities between -norms of functions and , where is the Hardy operator, is its dual, and is a nonnegative measurable function on In an equivalent form, it gives sharp constants in the two-sided relationships between -norms of functions and , where is a nonnegative nonincreasing function on with In particular, it provides an alternative proof of a result obtained by Kruglyak and Setterqvist (Proc Am Math Soc 136:2005-2013, 2008) for and by Boza and Soria (J Funct Anal 260:1020-1028, 2011) for all , and gives a sharp version of this result for 1 < p < 2.

Place, publisher, year, edition, pages
Springer, 2014
Keywords
Hardy operator, Dual operator, Best constants
National Category
Mathematics
Identifiers
urn:nbn:se:kau:diva-41542 (URN)10.1007/s10231-012-0283-9 (DOI)000333199900007 ()
Available from: 2016-04-25 Created: 2016-04-11 Last updated: 2017-11-30Bibliographically approved
Kolyada, V. (2014). Sections of Functions and Sobolev-Type Inequalities. Proceedings of the Steklov Institute of Mathematics, 284(1), 192-203
Open this publication in new window or tab >>Sections of Functions and Sobolev-Type Inequalities
2014 (English)In: Proceedings of the Steklov Institute of Mathematics, ISSN 0081-5438, E-ISSN 1531-8605, Vol. 284, no 1, p. 192-203Article in journal (Refereed) Published
Abstract [en]

We study functions of two variables whose sections by the lines parallel to the coordinate axis satisfy the Lipschitz condition of order 0 < alpha a parts per thousand currency sign 1. We prove that if for a function f the Lip alpha-norms of these sections belong to the Lorentz space L (p,1)(a"e) (p = 1/alpha), then f can be modified on a set of measure zero so as to become bounded and uniformly continuous on a"e(2). For alpha = 1 this gives an extension of Sobolev's theorem on continuity of functions of the space W (1) (2,2) (a"e(2)). We show that the exterior L (p,1)-norm cannot be replaced by a weaker Lorentz L (p,q) -norm with q > 1.

Place, publisher, year, edition, pages
Maik Nauka/Interperiodica, 2014
National Category
Mathematics
Identifiers
urn:nbn:se:kau:diva-41538 (URN)10.1134/S0081543814010131 (DOI)000335559000012 ()
Available from: 2016-04-25 Created: 2016-04-11 Last updated: 2017-11-30Bibliographically approved
Kolyada, V. (2013). My First Meetings with Konstantin Oskolkov (1ed.). In: Dmitriy Bilyk, Laura De Carli, Alexander Petukhov, Alexander M. Stokolos, Brett D. Wick (Ed.), Recent Advances in Harmonic Analysis and Applications: In honor of Konstantin Oskolkov (pp. 27-29). Springer, 25
Open this publication in new window or tab >>My First Meetings with Konstantin Oskolkov
2013 (English)In: Recent Advances in Harmonic Analysis and Applications: In honor of Konstantin Oskolkov / [ed] Dmitriy Bilyk, Laura De Carli, Alexander Petukhov, Alexander M. Stokolos, Brett D. Wick, Springer, 2013, 1, Vol. 25, p. 27-29Chapter in book (Refereed)
Abstract [en]

This note tells about our first meetings with Konstatin Oskolkov. We discuss also optimal estimates of the rate of convergence of Fourier series obtained by Oskolkov in 1975.

Place, publisher, year, edition, pages
Springer, 2013 Edition: 1
Series
Springer Proceedings in Mathematics & Statistics, ISSN 2194-1017, E-ISSN 2194-1009 ; 25
Keywords
Optimal estimates; Rate of convergence, Fourier series
National Category
Mathematics Algebra and Logic
Research subject
Mathematics
Identifiers
urn:nbn:se:kau:diva-44260 (URN)10.1007/978-1-4614-4565-4_3 (DOI)2-s2.0-84883428557 (Scopus ID)
Available from: 2016-07-01 Created: 2016-07-01 Last updated: 2017-10-30Bibliographically approved
Kolyada, V. (2013). On limiting relations for capacities. Real Analysis Exchange, 38(1), 211-240
Open this publication in new window or tab >>On limiting relations for capacities
2013 (English)In: Real Analysis Exchange, ISSN 0147-1937, Vol. 38, no 1, p. 211-240Article in journal (Refereed) Published
Place, publisher, year, edition, pages
Michigan State University Press, 2013
National Category
Natural Sciences
Research subject
Mathematics
Identifiers
urn:nbn:se:kau:diva-29004 (URN)
Available from: 2013-09-11 Created: 2013-09-11 Last updated: 2016-10-06Bibliographically approved
Kolyada, V. (2012). Iterated rearrangements and Gagliardo-Sobolev type inequalities. Journal of Mathematical Analysis and Applications, 387(1), 335-348
Open this publication in new window or tab >>Iterated rearrangements and Gagliardo-Sobolev type inequalities
2012 (English)In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, Vol. 387, no 1, p. 335-348Article in journal (Refereed) Published
Abstract [en]

In this paper we consider Lorentz type spaces defined in terms of iterated rearrangements of functions of several variables (σ is a permutation of {1,…,n}). Further, we study Fournier–Gagliardo mixed norm spaces V(Rn) closely related to Sobolev spaces . We prove estimate of via ‖fV with the sharp constant. In particular, this gives a refinement of the known Sobolev type inequalities for the space .

Place, publisher, year, edition, pages
Elsevier, 2012
Keywords
Rearrangements; Embeddings; Sharp constants; Mixed norms
National Category
Mathematical Analysis Other Physics Topics
Identifiers
urn:nbn:se:kau:diva-15784 (URN)10.1016/j.jmaa.2011.08.077 (DOI)000296115100027 ()
Available from: 2012-11-26 Created: 2012-11-26 Last updated: 2018-07-13Bibliographically approved
Kolyada, V. (2012). On Fubini type property in Lorentz spaces. In: Bilyk, D. (Ed.), Recent Advances in Harmonic Analysis and Applications: (pp. 171-179). New York: Springer
Open this publication in new window or tab >>On Fubini type property in Lorentz spaces
2012 (English)In: Recent Advances in Harmonic Analysis and Applications / [ed] Bilyk, D., New York: Springer, 2012, p. 171-179Chapter in book (Refereed)
Abstract [en]

We study Fubini-type property for Lorentz spaces L p,r (R 2 ) . This problem is twofold. First we assume that all linear sections of a function f in directions of coordinate axes belong to L p,r (R) , and their one-dimensional Lp, r-norms belong to L p,r (R). We show that for pr it does not imply that f∈L p,r (R 2 ) (this complements one result by Cwikel). Conversely, we assume that f∈L p,r (R 2 ) , and we show that then for r < p almost all linear sections of f belong to L p,r (R) , but for p < r all linear sections may have infinite one-dimensional Lp, r-norms

Place, publisher, year, edition, pages
New York: Springer, 2012
Series
Springer Proceedings in Mathematics and Statistics, ISSN 2194-1009, E-ISSN 1024003 ; 25
National Category
Mathematical Analysis
Identifiers
urn:nbn:se:kau:diva-15785 (URN)10.1007/978-1-4614-4565-4_16 (DOI)978-1-4614-4564-7 (ISBN)978-1-4614-4565-4 (ISBN)
Available from: 2012-11-26 Created: 2012-11-26 Last updated: 2018-07-17Bibliographically approved
Kolyada, V. & Lind, M. (2012). On moduli of p-continuity. Acta Mathematica Hungarica, 137(3), 191-213
Open this publication in new window or tab >>On moduli of p-continuity
2012 (English)In: Acta Mathematica Hungarica, ISSN 0236-5294, E-ISSN 1588-2632, Vol. 137, no 3, p. 191-213Article in journal (Refereed) Published
Abstract [en]

Moduli of p-continuity provide a measure of fractional smoothness of functions via p-variation. We prove sharp estimates of the modulus of p-continuty in terms of the modulus of q-continuity (1<p<q<\infty).

Place, publisher, year, edition, pages
Springer, 2012
Keywords
p-variation, modulus of p-continuty, fractional smoothness, class of functions, embedding
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
urn:nbn:se:kau:diva-15249 (URN)10.1007/s10474-012-0246-z (DOI)000309856000003 ()
Available from: 2012-10-23 Created: 2012-10-23 Last updated: 2017-12-07Bibliographically approved
Organisations
Identifiers
ORCID iD: ORCID iD iconorcid.org/0000-0001-5459-0796

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