Continuity of Sobolev functions of variable exponent on metric spaces
Yoshihiro Mizuta and Tetsu Shimomura
Source: Proc. Japan Acad. Ser. A Math. Sci. Volume 80, Number 6
(2004), 96-99.
Abstract
Our aim in this paper is to discuss continuity of Sobolev functions of variable exponent on metric spaces in the limiting case of Sobolev's imbedding theorem.
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Primary Subjects:
46E35
Keywords: Hölder continuity; differentiability; weighted Sobolev spaces; $A_p$-weight; $p$-Poincaré inequality; Sobolev's imbedding theorem of variable exponent
Full-text: Open access
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.pja/1116014784
Mathematical Reviews number (MathSciNet): MR2075449
Zentralblatt MATH identifier: 02138346
Digital Object Identifier: doi:10.3792/pjaa.80.96
References
Björn, J.: $L^q$-Differentials for weighted spaces. Michigan Math. J., 47, 151--161 (2000).
Mathematical Reviews (MathSciNet): MR1755262
Digital Object Identifier: doi:10.1307/mmj/1030374674
Project Euclid: euclid.mmj/1030374674
Hajłasz, P., and Koskela, P.: Sobolev met Poincaré. Mem. Amer. Math. Soc., 145, 1--101 (2000).
Mathematical Reviews (MathSciNet): MR1683160
Heinonen, J., Kilpeläinen, T., and Martio, O.: Nonlinear Potential Theory of Degenerate Elliptic Equations. Clarendon Press/Oxford Univ. Press, New York (1993).
Mathematical Reviews (MathSciNet): MR1207810
Zentralblatt MATH: 0780.31001
Kováčik, O., and Rákosník, J.: On spaces $L^p(x)$ and $W^k,p(x)$. Czechoslovak Math. J., 41 (116), 592--618 (1991).
Mathematical Reviews (MathSciNet): MR1134951
Mizuta, Y.: Continuity properties of Riesz potentials and boundary limits of Beppo Levi functions. Math. Scand., 63, 238--260 (1988).
Mathematical Reviews (MathSciNet): MR1018814
Mizuta, Y.: Continuity properties of potentials and Beppo-Levi-Deny functions. Hiroshima Math. J., 23, 79--153 (1993).
Mathematical Reviews (MathSciNet): MR1211771
Mizuta, Y.: Integral representations, differentiability properties and limits at infinity for Beppo Levi functions. Potential Anal., 6, 237--276 (1997).
Mathematical Reviews (MathSciNet): MR1452545
Digital Object Identifier: doi:10.1023/A:1017996900877
Zentralblatt MATH: 0885.31004
Mizuta, Y., and Shimomura, T.: Differentiability and Hölder continuity of Riesz potentials of Orlicz functions. Analysis (Munich), 20, 201--223 (2000).
Mathematical Reviews (MathSciNet): MR1778254
Mizuta, Y., and Shimomura, T.: Continuity and differentiability for weighted Sobolev spaces. Proc. Amer. Math. Soc., 130, 2985--2994 (2002).
Mathematical Reviews (MathSciNet): MR1908921
Digital Object Identifier: doi:10.1090/S0002-9939-02-06410-9
Zentralblatt MATH: 1029.46032
Shimomura, T., and Mizuta, Y.: Taylor expansion of Riesz potentials. Hiroshima Math. J., 25, 595--621 (1995).
Mathematical Reviews (MathSciNet): MR1364077
Stein, E. M.: Singular Integrals and Differentiability Properties of Functions. Princeton Mathematical Series, no. 30, Princeton Univ. Press, Princeton, N.J. (1970).
Mathematical Reviews (MathSciNet): MR290095
Zentralblatt MATH: 0207.13501
Proceedings of the Japan Academy, Series A, Mathematical Sciences
