Ändra sökning
Länk till posten
Permanent länk

Direktlänk
BETA
Publikationer (10 of 26) Visa alla publikationer
Kolyada, V. (2020). On the optimal relationships between L-P-norms for the Hardy operator and its dual for decreasing functions. Journal of Approximation Theory, 252, Article ID UNSP 105362.
Öppna denna publikation i ny flik eller fönster >>On the optimal relationships between L-P-norms for the Hardy operator and its dual for decreasing functions
2020 (Engelska)Ingår i: Journal of Approximation Theory, ISSN 0021-9045, E-ISSN 1096-0430, Vol. 252, artikel-id UNSP 105362Artikel i tidskrift (Refereegranskat) Published
Abstract [en]

We prove sharp inequalities between L-P-norms (1 < p < infinity) of functions Hf and H*f, where H is the Hardy operator, H* is its dual, and f is a nonnegative nonincreasing function on (0, infinity). In particular, we extend one result obtained for integer p >= 2 by Boza and Soria (2019), to the whole range of values p >= 2. (C) 2019 Elsevier Inc. All rights reserved.

Ort, förlag, år, upplaga, sidor
Elsevier, 2020
Nyckelord
Hardy operator, Dual operator, Best constants
Nationell ämneskategori
Matematik
Identifikatorer
urn:nbn:se:kau:diva-77418 (URN)10.1016/j.jat.2019.105362 (DOI)000517849400006 ()
Tillgänglig från: 2020-04-02 Skapad: 2020-04-02 Senast uppdaterad: 2020-04-27Bibliografiskt granskad
Kolyada, V. (2019). Embedding theorems for Sobolev and Hardy-Sobolev spaces and estimates of Fourier transforms. Annali di Matematica Pura ed Applicata, 198(2), 615-637
Öppna denna publikation i ny flik eller fönster >>Embedding theorems for Sobolev and Hardy-Sobolev spaces and estimates of Fourier transforms
2019 (Engelska)Ingår i: Annali di Matematica Pura ed Applicata, ISSN 0373-3114, E-ISSN 1618-1891, Vol. 198, nr 2, s. 615-637Artikel i tidskrift (Refereegranskat) Published
Abstract [en]

We prove embeddings of Sobolev and Hardy-Sobolev spaces into Besov spaces built upon certain mixed norms. This gives an improvement of the known embeddings into usual Besov spaces. Applying these results, we obtain Oberlin-type estimates of Fourier transforms for functions in Sobolev spaces W11(Rn).

Ort, förlag, år, upplaga, sidor
Springer, 2019
Nationell ämneskategori
Matematik
Forskningsämne
Matematik
Identifikatorer
urn:nbn:se:kau:diva-71809 (URN)10.1007/s10231-018-0792-2 (DOI)000462444500016 ()
Tillgänglig från: 2019-04-11 Skapad: 2019-04-11 Senast uppdaterad: 2020-05-11Bibliografiskt granskad
Kolyada, V. (2019). On the Cèsaro and Copson Norms of Nonnegative Sequences. Ukrainian Mathematical Journal, 71(2), 248-258
Öppna denna publikation i ny flik eller fönster >>On the Cèsaro and Copson Norms of Nonnegative Sequences
2019 (Engelska)Ingår i: Ukrainian Mathematical Journal, ISSN 0041-5995, E-ISSN 1573-9376, Vol. 71, nr 2, s. 248-258Artikel i tidskrift (Refereegranskat) 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 &lt; p &lt; 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.

Ort, förlag, år, upplaga, sidor
Springer, 2019
Nationell ämneskategori
Matematik
Forskningsämne
Matematik
Identifikatorer
urn:nbn:se:kau:diva-75741 (URN)10.1007/s11253-019-01642-7 (DOI)000509896300008 ()2-s2.0-85073948250 (Scopus ID)
Tillgänglig från: 2019-11-12 Skapad: 2019-11-12 Senast uppdaterad: 2020-02-20Bibliografiskt granskad
Kolyada, V. & Soria, J. (2016). Mixed Norms and Iterated Rearrangements. Zeitschrift für Analysis und ihre Anwendungen, 35(2), 119-138
Öppna denna publikation i ny flik eller fönster >>Mixed Norms and Iterated Rearrangements
2016 (Engelska)Ingår i: Zeitschrift für Analysis und ihre Anwendungen, ISSN 0232-2064, E-ISSN 1661-4534, Vol. 35, nr 2, s. 119-138Artikel i tidskrift (Refereegranskat) 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.

Ort, förlag, år, upplaga, sidor
EUROPEAN MATHEMATICAL SOC, 2016
Nyckelord
Rearrangements, embeddings, mixed norms, Lorentz spaces
Nationell ämneskategori
Matematik
Forskningsämne
Matematik
Identifikatorer
urn:nbn:se:kau:diva-54916 (URN)10.4171/ZAA/1557 (DOI)000388453600001 ()
Tillgänglig från: 2017-06-08 Skapad: 2017-06-08 Senast uppdaterad: 2019-12-02Bibliografiskt granskad
Kolyada, V. & Perez Lazaro, F. J. (2014). On Gagliardo-Nirenberg Type Inequalities. Journal of Fourier Analysis and Applications, 20(3), 577-607
Öppna denna publikation i ny flik eller fönster >>On Gagliardo-Nirenberg Type Inequalities
2014 (Engelska)Ingår i: Journal of Fourier Analysis and Applications, ISSN 1069-5869, E-ISSN 1531-5851, Vol. 20, nr 3, s. 577-607Artikel i tidskrift (Refereegranskat) 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.

Ort, förlag, år, upplaga, sidor
Springer, 2014
Nyckelord
Gagliardo-Nirenberg inequality, Sobolev spaces, Besov spaces, Triebel-Lizorkin spaces
Nationell ämneskategori
Matematik
Forskningsämne
Matematik
Identifikatorer
urn:nbn:se:kau:diva-41523 (URN)10.1007/s00041-014-9320-y (DOI)000337789300007 ()
Tillgänglig från: 2016-04-25 Skapad: 2016-04-11 Senast uppdaterad: 2020-05-20Bibliografiskt granskad
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
Öppna denna publikation i ny flik eller fönster >>Optimal relationships between L-p-norms for the Hardy operator and its dual
2014 (Engelska)Ingår i: Annali di Matematica Pura ed Applicata, ISSN 0373-3114, E-ISSN 1618-1891, Vol. 193, nr 2, s. 423-430Artikel i tidskrift (Refereegranskat) 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.

Ort, förlag, år, upplaga, sidor
Springer, 2014
Nyckelord
Hardy operator, Dual operator, Best constants
Nationell ämneskategori
Matematik
Forskningsämne
Matematik
Identifikatorer
urn:nbn:se:kau:diva-41542 (URN)10.1007/s10231-012-0283-9 (DOI)000333199900007 ()
Tillgänglig från: 2016-04-25 Skapad: 2016-04-11 Senast uppdaterad: 2020-05-20Bibliografiskt granskad
Kolyada, V. (2014). Sections of Functions and Sobolev-Type Inequalities. Proceedings of the Steklov Institute of Mathematics, 284(1), 192-203
Öppna denna publikation i ny flik eller fönster >>Sections of Functions and Sobolev-Type Inequalities
2014 (Engelska)Ingår i: Proceedings of the Steklov Institute of Mathematics, ISSN 0081-5438, E-ISSN 1531-8605, Vol. 284, nr 1, s. 192-203Artikel i tidskrift (Refereegranskat) 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.

Ort, förlag, år, upplaga, sidor
Maik Nauka/Interperiodica, 2014
Nationell ämneskategori
Matematik
Forskningsämne
Matematik
Identifikatorer
urn:nbn:se:kau:diva-41538 (URN)10.1134/S0081543814010131 (DOI)000335559000012 ()
Tillgänglig från: 2016-04-25 Skapad: 2016-04-11 Senast uppdaterad: 2020-05-20Bibliografiskt granskad
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
Öppna denna publikation i ny flik eller fönster >>My First Meetings with Konstantin Oskolkov
2013 (Engelska)Ingår i: 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, s. 27-29Kapitel i bok, del av antologi (Refereegranskat)
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.

Ort, förlag, år, upplaga, sidor
Springer, 2013 Upplaga: 1
Serie
Springer Proceedings in Mathematics & Statistics, ISSN 2194-1017, E-ISSN 2194-1009 ; 25
Nyckelord
Optimal estimates; Rate of convergence, Fourier series
Nationell ämneskategori
Matematik Algebra och logik
Forskningsämne
Matematik
Identifikatorer
urn:nbn:se:kau:diva-44260 (URN)10.1007/978-1-4614-4565-4_3 (DOI)2-s2.0-84883428557 (Scopus ID)
Tillgänglig från: 2016-07-01 Skapad: 2016-07-01 Senast uppdaterad: 2017-10-30Bibliografiskt granskad
Kolyada, V. (2013). On limiting relations for capacities. Real Analysis Exchange, 38(1), 211-240
Öppna denna publikation i ny flik eller fönster >>On limiting relations for capacities
2013 (Engelska)Ingår i: Real Analysis Exchange, ISSN 0147-1937, Vol. 38, nr 1, s. 211-240Artikel i tidskrift (Refereegranskat) Published
Ort, förlag, år, upplaga, sidor
Michigan State University Press, 2013
Nationell ämneskategori
Matematik
Forskningsämne
Matematik
Identifikatorer
urn:nbn:se:kau:diva-29004 (URN)
Tillgänglig från: 2013-09-11 Skapad: 2013-09-11 Senast uppdaterad: 2020-04-03Bibliografiskt granskad
Kolyada, V. (2012). Iterated rearrangements and Gagliardo-Sobolev type inequalities. Journal of Mathematical Analysis and Applications, 387(1), 335-348
Öppna denna publikation i ny flik eller fönster >>Iterated rearrangements and Gagliardo-Sobolev type inequalities
2012 (Engelska)Ingår i: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, Vol. 387, nr 1, s. 335-348Artikel i tidskrift (Refereegranskat) 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 .

Ort, förlag, år, upplaga, sidor
Elsevier, 2012
Nyckelord
Rearrangements; Embeddings; Sharp constants; Mixed norms
Nationell ämneskategori
Matematisk analys Annan fysik
Identifikatorer
urn:nbn:se:kau:diva-15784 (URN)10.1016/j.jmaa.2011.08.077 (DOI)000296115100027 ()
Tillgänglig från: 2012-11-26 Skapad: 2012-11-26 Senast uppdaterad: 2018-07-13Bibliografiskt granskad
Organisationer
Identifikatorer
ORCID-id: ORCID iD iconorcid.org/0000-0001-5459-0796

Sök vidare i DiVA

Visa alla publikationer