An optimal limiting Sobolev inequality

Author:
Andrei Biryuk

Journal:
Proc. Amer. Math. Soc. **138** (2010), 1461-1470

MSC (2000):
Primary 52A40, 46E35; Secondary 46E30, 26D10

Published electronically:
November 13, 2009

MathSciNet review:
2578540

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Abstract | References | Similar Articles | Additional Information

Abstract: The main goal of this paper is to prove an optimal limiting Sobolev inequality in two dimensions for Hölder continuous functions. Additionally, from this inequality we derive the double logarithmic inequality

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Additional Information

**Andrei Biryuk**

Affiliation:
Departamento de Matematica, Instituto Superior Técnico, Centro de Análise Mate- mática, Geometria e Sistemas Dinâmicos, Lisbon, Portugal

DOI:
http://dx.doi.org/10.1090/S0002-9939-09-10159-4

Keywords:
Limiting Sobolev embedding theorems,
double logarithmic inequality.

Received by editor(s):
March 3, 2009

Received by editor(s) in revised form:
August 10, 2009

Published electronically:
November 13, 2009

Additional Notes:
The author is supported in part by CAMGSD and FCT/POCTI-POCI/FEDER. Part of the research (Theorem 3) was done while the author was a member of McMaster University in 2004. The author was supported in part by a CRC postdoctoral fellowship of McMaster University.

Communicated by:
Walter Craig

Article copyright:
© Copyright 2009
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.