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Kolyada, Viktororcid.org/0000-0001-5459-0796

Open this publication in new window or tab >>On the Cèsaro and Copson Norms of Nonnegative Sequences### Kolyada, Viktor

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_0_j_idt188_some",{id:"formSmash:j_idt184:0:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_0_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_0_j_idt188_otherAuthors",{id:"formSmash:j_idt184:0:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_0_j_idt188_otherAuthors",multiple:true}); 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]

##### 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)
#####

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Available from: 2019-11-12 Created: 2019-11-12 Last updated: 2020-02-20Bibliographically approved

Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).

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.

Open this publication in new window or tab >>Mixed Norms and Iterated Rearrangements### Kolyada, Viktor

### Soria, Javier

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_1_j_idt188_some",{id:"formSmash:j_idt184:1:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_1_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_1_j_idt188_otherAuthors",{id:"formSmash:j_idt184:1:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_1_j_idt188_otherAuthors",multiple:true}); 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]

##### 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 ()
#####

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Available from: 2017-06-08 Created: 2017-06-08 Last updated: 2019-12-02Bibliographically approved

Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).

Univ Barcelona, Dept Appl Math & Anal, Gran Via 585, E-08007 Barcelona, Spain..

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

Open this publication in new window or tab >>On Gagliardo-Nirenberg Type Inequalities### Kolyada, Viktor

### Perez Lazaro, F. J.

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_2_j_idt188_some",{id:"formSmash:j_idt184:2:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_2_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_2_j_idt188_otherAuthors",{id:"formSmash:j_idt184:2:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_2_j_idt188_otherAuthors",multiple:true}); 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]

##### 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 ()
#####

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Available from: 2016-04-25 Created: 2016-04-11 Last updated: 2017-11-30Bibliographically approved

Karlstad University, Faculty of Technology and Science, Department of Mathematics.

Univ La Rioja, Dept Matemat & Comp, Logrono 26004, Spain..

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.

Open this publication in new window or tab >>Optimal relationships between L-p-norms for the Hardy operator and its dual### Kolyada, Viktor

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_3_j_idt188_some",{id:"formSmash:j_idt184:3:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_3_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_3_j_idt188_otherAuthors",{id:"formSmash:j_idt184:3:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_3_j_idt188_otherAuthors",multiple:true}); 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]

##### 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 ()
#####

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Available from: 2016-04-25 Created: 2016-04-11 Last updated: 2017-11-30Bibliographically approved

Karlstad University, Faculty of Technology and Science, Department of Mathematics.

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.

Open this publication in new window or tab >>Sections of Functions and Sobolev-Type Inequalities### Kolyada, Viktor

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_4_j_idt188_some",{id:"formSmash:j_idt184:4:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_4_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_4_j_idt188_otherAuthors",{id:"formSmash:j_idt184:4:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_4_j_idt188_otherAuthors",multiple:true}); 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]

##### 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 ()
#####

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Available from: 2016-04-25 Created: 2016-04-11 Last updated: 2017-11-30Bibliographically approved

Karlstad University, Faculty of Technology and Science, Department of Mathematics.

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.

Open this publication in new window or tab >>My First Meetings with Konstantin Oskolkov### Kolyada, Viktor

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_5_j_idt188_some",{id:"formSmash:j_idt184:5:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_5_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_5_j_idt188_otherAuthors",{id:"formSmash:j_idt184:5:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_5_j_idt188_otherAuthors",multiple:true}); 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]

##### 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)
#####

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Available from: 2016-07-01 Created: 2016-07-01 Last updated: 2017-10-30Bibliographically approved

Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.

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.

Open this publication in new window or tab >>On limiting relations for capacities### Kolyada, Viktor

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_6_j_idt188_some",{id:"formSmash:j_idt184:6:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_6_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_6_j_idt188_otherAuthors",{id:"formSmash:j_idt184:6:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_6_j_idt188_otherAuthors",multiple:true}); 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)
#####

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Available from: 2013-09-11 Created: 2013-09-11 Last updated: 2016-10-06Bibliographically approved

Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.

Open this publication in new window or tab >>Iterated rearrangements and Gagliardo-Sobolev type inequalities### Kolyada, Viktor

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_7_j_idt188_some",{id:"formSmash:j_idt184:7:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_7_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_7_j_idt188_otherAuthors",{id:"formSmash:j_idt184:7:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_7_j_idt188_otherAuthors",multiple:true}); 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]

##### 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 ()
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Available from: 2012-11-26 Created: 2012-11-26 Last updated: 2018-07-13Bibliographically approved

Karlstad University, Faculty of Technology and Science, Department of Mathematics.

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*(*R**n*) closely related to Sobolev spaces . We prove estimate of via ‖*f**V*_{‖} with the sharp constant. In particular, this gives a refinement of the known Sobolev type inequalities for the space .

Open this publication in new window or tab >>On Fubini type property in Lorentz spaces### Kolyada, Viktor

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_8_j_idt188_some",{id:"formSmash:j_idt184:8:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_8_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_8_j_idt188_otherAuthors",{id:"formSmash:j_idt184:8:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_8_j_idt188_otherAuthors",multiple:true}); 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]

##### 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)
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Available from: 2012-11-26 Created: 2012-11-26 Last updated: 2018-07-17Bibliographically approved

Karlstad University, Faculty of Technology and Science, Department of Mathematics.

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 *L*^{p, r}-norms belong to L p,r (R). We show that for *p* ≠ *r* 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 *L*^{p, r}-norms

Open this publication in new window or tab >>On moduli of p-continuity### Kolyada, Viktor

### Lind, Martin

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_9_j_idt188_some",{id:"formSmash:j_idt184:9:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_9_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_9_j_idt188_otherAuthors",{id:"formSmash:j_idt184:9:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_9_j_idt188_otherAuthors",multiple:true}); 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]

##### 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 ()
#####

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Available from: 2012-10-23 Created: 2012-10-23 Last updated: 2017-12-07Bibliographically approved

Karlstad University, Faculty of Technology and Science, Department of Mathematics.

Karlstad University, Faculty of Technology and Science, Department of Mathematics.

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).