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Continuity and differentiability for weighted Sobolev spaces
Author(s):
Yoshihiro
Mizuta;
Tetsu
Shimomura
Journal:
Proc. Amer. Math. Soc.
130
(2002),
2985-2994.
MSC (2000):
Primary 46E35
Posted:
March 14, 2002
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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.
References:
- 1.
- J. Björn,
 -Differentials for weighted spaces, Michigan Math.J. 47 (2000), 151-161. - 2.
- P. Haj
 asz and P. Koskela, Sobolev met Poincaré, Mem. Amer. Math. Soc. 145 (2000). MR 2000j:46063 - 3.
- J. Heinonen, T. Kilpeläinen and O. Martio, Nonlinear potential theory of degenerate elliptic equations, Clarendon Press, 1993.MR 94e:31003
- 4.
- Y. Mizuta, Continuity properties of Riesz potentials and boundary limits of Beppo Levi functions, Math. Scand. 63 (1988), 238-260.MR 90m:31010
- 5.
- Y. Mizuta, Continuity properties of potentials and Beppo-Levi-Deny functions, Hiroshima Math. J. 23 (1993), 79-153.MR 94d:31005
- 6.
- Y. Mizuta, Integral representations, differentiability properties and limits at infinity for Beppo Levi functions, Potential Analysis 6 (1997), 237-276.MR 98k:31007
- 7.
- Y. Mizuta and T. Shimomura, Differentiability and Hölder continuity of Riesz potentials of Orlicz functions, Analysis 20 (2000), 201-223.MR 2001h:46052
- 8.
- T. Shimomura and Y. Mizuta, Taylor expansion of Riesz potentials, Hiroshima Math. J. 25 (1995), 595-621.MR 97d:31009
- 9.
- E. M. Stein, Singular integrals and differentiability properties of functions, Princeton Univ. Press, Princeton, 1970.MR 44:7280
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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:
10.1090/S0002-9939-02-06410-9
PII:
S 0002-9939(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
Posted:
March 14, 2002
Communicated by:
Juha M. Heinonen
Copyright of article:
Copyright
2002,
American Mathematical Society
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