Weighted Orlicz-Riesz capacity of balls
HTML articles powered by AMS MathViewer
- by Yoshihiro Mizuta, Takao Ohno and Tetsu Shimomura PDF
- Proc. Amer. Math. Soc. 138 (2010), 4291-4302 Request permission
Abstract:
Our aim in this paper is to estimate the weighted Orlicz-Riesz capacity of balls.References
- David R. Adams, Weighted capacity and the Choquet integral, Proc. Amer. Math. Soc. 102 (1988), no. 4, 879–887. MR 934860, DOI 10.1090/S0002-9939-1988-0934860-7
- David R. Adams and Lars Inge Hedberg, Function spaces and potential theory, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 314, Springer-Verlag, Berlin, 1996. MR 1411441, DOI 10.1007/978-3-662-03282-4
- David R. Adams and Ritva Hurri-Syrjänen, Vanishing exponential integrability for functions whose gradients belong to $L^n(\log (e+L))^\alpha$, J. Funct. Anal. 197 (2003), no. 1, 162–178. MR 1957679, DOI 10.1016/S0022-1236(02)00092-7
- David R. Adams and Ritva Hurri-Syrjänen, Capacity estimates, Proc. Amer. Math. Soc. 131 (2003), no. 4, 1159–1167. MR 1948107, DOI 10.1090/S0002-9939-02-06622-4
- N. Aïssaoui and A. Benkirane, Capacités dans les espaces d’Orlicz, Ann. Sci. Math. Québec 18 (1994), no. 1, 1–23 (French, with English and French summaries). MR 1273865
- Colin Bennett and Robert Sharpley, Interpolation of operators, Pure and Applied Mathematics, vol. 129, Academic Press, Inc., Boston, MA, 1988. MR 928802
- David E. Edmunds and W. Desmond Evans, Hardy operators, function spaces and embeddings, Springer Monographs in Mathematics, Springer-Verlag, Berlin, 2004. MR 2091115, DOI 10.1007/978-3-662-07731-3
- T. Futamura, Y. Mizuta, T. Ohno and T. Shimomura, Orlicz-Sobolev capacity of balls, to appear in Illinois J. Math.
- 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
- Jani Joensuu, On null sets of Sobolev-Orlicz capacities, Illinois J. Math. 52 (2008), no. 4, 1195–1211. MR 2595762
- Jani Joensuu, Orlicz-Sobolev capacities and their null sets, Rev. Mat. Complut. 23 (2010), no. 1, 217–232. MR 2578579, DOI 10.1007/s13163-009-0011-1
- J. Joensuu, Estimates for certain Orlicz-Sobolev capacities of an Euclidean ball, Nonlinear Anal. 72 (2010), 4316-4330.
- Tero Kilpeläinen, Weighted Sobolev spaces and capacity, Ann. Acad. Sci. Fenn. Ser. A I Math. 19 (1994), no. 1, 95–113. MR 1246890
- S. E. Kuznetsov, Removable singularities for $Lu=\Psi (u)$ and Orlicz capacities, J. Funct. Anal. 170 (2000), no. 2, 428–449. MR 1740658, DOI 10.1006/jfan.1999.3480
- Norman G. Meyers, A theory of capacities for potentials of functions in Lebesgue classes, Math. Scand. 26 (1970), 255–292 (1971). MR 277741, DOI 10.7146/math.scand.a-10981
- Yoshihiro Mizuta, Continuity properties of potentials and Beppo-Levi-Deny functions, Hiroshima Math. J. 23 (1993), no. 1, 79–153. MR 1211771
- Yoshihiro Mizuta, Potential theory in Euclidean spaces, GAKUTO International Series. Mathematical Sciences and Applications, vol. 6, Gakk\B{o}tosho Co., Ltd., Tokyo, 1996. MR 1428685
- Y. Mizuta, E. Nakai, T. Ohno and T. Shimomura, Sobolev embeddings for Riesz potentials of functions in Morrey spaces $L^{(1,\varphi )}(G)$, to appear in J. Math. Soc. Japan.
- 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
- Yoshihiro Mizuta and Tetsu Shimomura, Vanishing exponential integrability for Riesz potentials of functions in Orlicz classes, Illinois J. Math. 51 (2007), no. 4, 1039–1060. MR 2417414
- Yoshihiro Mizuta and Tetsu Shimomura, Continuity properties of Riesz potentials of Orlicz functions, Tohoku Math. J. (2) 61 (2009), no. 2, 225–240. MR 2541407, DOI 10.2748/tmj/1245849445
- William P. Ziemer, Weakly differentiable functions, Graduate Texts in Mathematics, vol. 120, Springer-Verlag, New York, 1989. Sobolev spaces and functions of bounded variation. MR 1014685, DOI 10.1007/978-1-4612-1015-3
Additional Information
- Yoshihiro Mizuta
- Affiliation: Department of Mathematics, Graduate School of Science, Hiroshima University, Higashi-Hiroshima 739-8521, Japan
- Email: yomizuta@hiroshima-u.ac.jp
- Takao Ohno
- Affiliation: General Arts, Hiroshima National College of Maritime Technology, Higashino Oosakikamijima Toyotagun 725-0231, Japan
- Address at time of publication: Department of Mathematics, Faculty of Education, Oita University, Dannohara Oita 870-1192, Japan
- Email: ohno@hiroshima-cmt.ac.jp
- Tetsu Shimomura
- Affiliation: Department of Mathematics, Graduate School of Education, Hiroshima University, Higashi-Hiroshima 739-8524, Japan
- MR Author ID: 356757
- Email: tshimo@hiroshima-u.ac.jp
- Received by editor(s): January 25, 2010
- Published electronically: May 26, 2010
- Communicated by: Tatiana Toro
- © Copyright 2010 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 138 (2010), 4291-4302
- MSC (2010): Primary 46E35; Secondary 46E30, 31B15
- DOI: https://doi.org/10.1090/S0002-9939-2010-10510-5
- MathSciNet review: 2680055