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Continuity and differentiability for weighted Sobolev spaces


Authors: Yoshihiro Mizuta and Tetsu Shimomura
Journal: Proc. Amer. Math. Soc. 130 (2002), 2985-2994
MSC (2000): Primary 46E35
Published electronically: March 14, 2002
MathSciNet review: 1908921
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Abstract: Our aim in this paper is to discuss continuity and differentiability of functions in weighted Sobolev spaces in the limiting case of Sobolev's imbedding theorem.


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Additional Information

Yoshihiro Mizuta
Affiliation: The Division of Mathematical and Information Sciences, Faculty of Integrated Arts and Sciences, Hiroshima University, Higashi-Hiroshima 739-8521, Japan

Tetsu Shimomura
Affiliation: Department of Mathematics, Graduate School of Education, Hiroshima University, Higashi-Hiroshima 739-8524, Japan

DOI: https://doi.org/10.1090/S0002-9939-02-06410-9
Keywords: H\"{o}lder continuity, differentiability, weighted Sobolev spaces, $A_p$-weight, $p$-Poincar\'{e} inequality, Sobolev's imbedding theorem
Received by editor(s): December 18, 2000
Received by editor(s) in revised form: May 9, 2001
Published electronically: March 14, 2002
Communicated by: Juha M. Heinonen
Article copyright: © Copyright 2002 American Mathematical Society