Continuity and differentiability for weighted Sobolev spaces
HTML articles powered by AMS MathViewer
- by Yoshihiro Mizuta and Tetsu Shimomura PDF
- Proc. Amer. Math. Soc. 130 (2002), 2985-2994 Request permission
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
- J. Björn, $L^q$-Differentials for weighted spaces, Michigan Math.J. 47 (2000), 151-161.
- Piotr Hajłasz and Pekka Koskela, Sobolev met Poincaré, Mem. Amer. Math. Soc. 145 (2000), no. 688, x+101. MR 1683160, DOI 10.1090/memo/0688
- Juha Heinonen, Tero Kilpeläinen, and Olli Martio, Nonlinear potential theory of degenerate elliptic equations, Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, New York, 1993. Oxford Science Publications. MR 1207810
- Yoshihiro Mizuta, Continuity properties of Riesz potentials and boundary limits of Beppo Levi functions, Math. Scand. 63 (1988), no. 2, 238–260. MR 1018814, DOI 10.7146/math.scand.a-12238
- Yoshihiro Mizuta, Continuity properties of potentials and Beppo-Levi-Deny functions, Hiroshima Math. J. 23 (1993), no. 1, 79–153. MR 1211771
- Yoshihiro Mizuta, Integral representations, differentiability properties and limits at infinity for Beppo Levi functions, Potential Anal. 6 (1997), no. 3, 237–267. MR 1452545, DOI 10.1023/A:1017996900877
- Yoshihiro Mizuta and Tetsu Shimomura, Differentiability and Hölder continuity of Riesz potentials of Orlicz functions, Analysis (Munich) 20 (2000), no. 3, 201–223. MR 1778254, DOI 10.1524/anly.2000.20.3.201
- Tetsu Shimomura and Yoshihiro Mizuta, Taylor expansion of Riesz potentials, Hiroshima Math. J. 25 (1995), no. 3, 595–621. MR 1364077
- Elias M. Stein, Singular integrals and differentiability properties of functions, Princeton Mathematical Series, No. 30, Princeton University Press, Princeton, N.J., 1970. MR 0290095
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
- MR Author ID: 356757
- 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
- © Copyright 2002 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 130 (2002), 2985-2994
- MSC (2000): Primary 46E35
- DOI: https://doi.org/10.1090/S0002-9939-02-06410-9
- MathSciNet review: 1908921