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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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  • 1. J. Björn, $L^q$-Differentials for weighted spaces, Michigan Math.J. 47 (2000), 151-161.
  • 2. P. Haj\lasz 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

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

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