Sharp Constants of Brézis-Gallouët-Wainger Type Inequalities with a Double Logarithmic Term on Bounded Domains in Besov and Triebel-Lizorkin Spaces

Sharp Constants of Brézis-Gallouët-Wainger Type Inequalities with a Double Logarithmic Term on Bounded Domains in Besov and Triebel-Lizorkin Spaces

<p>Abstract</p> <p>The present paper concerns the Sobolev embedding in the endpoint case. It is known that the embedding <inline-formula> <graphic file="1687-2770-2010-584521-i1.gif"/></inline-formula> fails for <inline-formula> <graphic file=&q...

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Main Authors: Sato Tokushi, Wadade Hidemitsu, Sawano Yoshihiro, Morii Kei
Format: Article
Language:English
Published: SpringerOpen 2010-01-01
Series:Boundary Value Problems
Online Access:http://www.boundaryvalueproblems.com/content/2010/584521
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spelling doaj-af7214a00e664c2dbf124a1cf1ecb4a02020-11-24T21:49:48ZengSpringerOpenBoundary Value Problems1687-27621687-27702010-01-0120101584521Sharp Constants of Br&#233;zis-Gallou&#235;t-Wainger Type Inequalities with a Double Logarithmic Term on Bounded Domains in Besov and Triebel-Lizorkin SpacesSato TokushiWadade HidemitsuSawano YoshihiroMorii Kei<p>Abstract</p> <p>The present paper concerns the Sobolev embedding in the endpoint case. It is known that the embedding <inline-formula> <graphic file="1687-2770-2010-584521-i1.gif"/></inline-formula> fails for <inline-formula> <graphic file="1687-2770-2010-584521-i2.gif"/></inline-formula>. Br&#233;zis-Gallou&#235;t-Wainger and some other authors quantified why this embedding fails by means of the H&#246;lder-Zygmund norm. In the present paper we will give a complete quantification of their results and clarify the sharp constants for the coefficients of the logarithmic terms in Besov and Triebel-Lizorkin spaces.</p>http://www.boundaryvalueproblems.com/content/2010/584521
collection DOAJ
language English
format Article
sources DOAJ
author Sato Tokushi
Wadade Hidemitsu
Sawano Yoshihiro
Morii Kei
spellingShingle Sato Tokushi
Wadade Hidemitsu
Sawano Yoshihiro
Morii Kei
Sharp Constants of Br&#233;zis-Gallou&#235;t-Wainger Type Inequalities with a Double Logarithmic Term on Bounded Domains in Besov and Triebel-Lizorkin Spaces
Boundary Value Problems
author_facet Sato Tokushi
Wadade Hidemitsu
Sawano Yoshihiro
Morii Kei
author_sort Sato Tokushi
title Sharp Constants of Br&#233;zis-Gallou&#235;t-Wainger Type Inequalities with a Double Logarithmic Term on Bounded Domains in Besov and Triebel-Lizorkin Spaces
title_short Sharp Constants of Br&#233;zis-Gallou&#235;t-Wainger Type Inequalities with a Double Logarithmic Term on Bounded Domains in Besov and Triebel-Lizorkin Spaces
title_full Sharp Constants of Br&#233;zis-Gallou&#235;t-Wainger Type Inequalities with a Double Logarithmic Term on Bounded Domains in Besov and Triebel-Lizorkin Spaces
title_fullStr Sharp Constants of Br&#233;zis-Gallou&#235;t-Wainger Type Inequalities with a Double Logarithmic Term on Bounded Domains in Besov and Triebel-Lizorkin Spaces
title_full_unstemmed Sharp Constants of Br&#233;zis-Gallou&#235;t-Wainger Type Inequalities with a Double Logarithmic Term on Bounded Domains in Besov and Triebel-Lizorkin Spaces
title_sort sharp constants of br&#233;zis-gallou&#235;t-wainger type inequalities with a double logarithmic term on bounded domains in besov and triebel-lizorkin spaces
publisher SpringerOpen
series Boundary Value Problems
issn 1687-2762
1687-2770
publishDate 2010-01-01
description <p>Abstract</p> <p>The present paper concerns the Sobolev embedding in the endpoint case. It is known that the embedding <inline-formula> <graphic file="1687-2770-2010-584521-i1.gif"/></inline-formula> fails for <inline-formula> <graphic file="1687-2770-2010-584521-i2.gif"/></inline-formula>. Br&#233;zis-Gallou&#235;t-Wainger and some other authors quantified why this embedding fails by means of the H&#246;lder-Zygmund norm. In the present paper we will give a complete quantification of their results and clarify the sharp constants for the coefficients of the logarithmic terms in Besov and Triebel-Lizorkin spaces.</p>
url http://www.boundaryvalueproblems.com/content/2010/584521
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AT wadadehidemitsu sharpconstantsofbr233zisgallou235twaingertypeinequalitieswithadoublelogarithmictermonboundeddomainsinbesovandtriebellizorkinspaces
AT sawanoyoshihiro sharpconstantsofbr233zisgallou235twaingertypeinequalitieswithadoublelogarithmictermonboundeddomainsinbesovandtriebellizorkinspaces
AT moriikei sharpconstantsofbr233zisgallou235twaingertypeinequalitieswithadoublelogarithmictermonboundeddomainsinbesovandtriebellizorkinspaces
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