Proceedings of the American Mathematical Society

Author(s): Wei-Shyan Tai
Journal: Proc. Amer. Math. Soc. 129 (2001), 699-711.
MSC (2000): Primary 26B35, 41A30, 46E35
Posted: November 3, 2000
Retrieve article in: PDF
This article is available free of charge

In this paper a capacitary weak type inequality for Sobolev functions is established and is applied to reprove some well-known results concerning Lebesgue points, Taylor expansions in the

-sense, and the Lusin type approximation of Sobolev functions.

1.: D. R. Adams, Maximal operator and capacity, Proc. Amer. Math. Soc., 34 (1972), 152-156. MR 50:2807
2.: D. R. Adams, Quasi-additivity and sets of finite $L^\varphi$ -capacity, Pacific J. Math., 79 (1978), 283-291. MR 81j:31006
3.: T. Bagby and W. P. Ziemer, Pointwise differentiability and absolute continuity, Trans. Amer. Math. Soc. 191 (1974), 129-148. MR 49:9129
4.: A. P. Calderón, Lebesgue spaces of differentiable functions and distributions, Proc. Symp. Pure Math., IV (1961), 33-49. MR 26:603
5.: A. P. Calderón and A. Zygmund, Local properties of solutions of elliptic partial differential equations, Studia Math., 20 (1961), 171-225. MR 25:310
6.: H. Federer, Geometric Measure Theory, Springer-Verlag, New York, Heidelberg, 1969. MR 41:1976
7.: H. Federer and W. P. Ziemer, The Lebesgue set of a function whose distribution derivatives are th power summable, Ind. Univ. Math. J., 22 (1972), 139-158. MR 55:8321
8.: Fon-Che Liu, A Lusin type property of Sobolev functions, Ind. Univ. Math. J., 26 (1977), 645-651.
9.: Fon-Che Liu and Wei-Shyan Tai, Maximal Steepness and Lusin type properties, Ric. Mat., 43 (1994), 365-384. MR 96c:26013
10.: B. Malgrange, Ideals of Differentiable Functions, Oxford University Press, 1966. MR 35:3446
11.: N. Meyers, Taylor expansion of Bessel potentials, Indiana Univ. Math. J., 23 (1974), 1043-1049. MR 50:980
12.: J. Michael and W. P. Ziemer, A Lusin type approximation of Sobolev functions by smooth functions, Contemporary Mathematics, AMS, 42 (1985), 135-167. MR 87e:46051
13.: E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton University Press, 1970. MR 44:7280
14.: H. Whitney, Analytic extensions of differentiable functions defined in closed sets, Trans. Amer. Math. Soc., 36 (1934), 63-89. CMP 95:18
15.: W. P. Ziemer, Uniform differentiability of Sobolev functions, Ind. Univ. Math. J., 37 (1988), 789-699. MR 90f:46054
16.: W. P. Ziemer, Weakly Differentiable Functions, Springer-Verlag, New York, 1989. MR 91e:46046

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 26B35, 41A30, 46E35

Wei-Shyan Tai
Affiliation: Department of Mathematics, National Chung Cheng University, Mingshiung, Chai Yi 61117, Taiwan, R.O.C.

DOI: 10.1090/S0002-9939-00-05976-1
PII: S 0002-9939(00)05976-1
Keywords: Sobolev functions, Riesz capacities, Lusin type properties
Received by editor(s): May 28, 1996
Posted: November 3, 2000
Additional Notes: This work was partially supported by Academia Sinica-Taipei, Taiwan, R.O.C. The author is deceased
Communicated by: Palle E. T. Jorgensen
Copyright of article: Copyright 2000, American Mathematical Society

			Journals Home Search Author Info Subscribe Tech Support Help
ISSN 1088-6826 (e) ISSN 0002-9939 (p)

Previous issue \| Table of contents \| Next issue Articles in press \| Recently posted articles \| Most recent issue \| All issues Previous Article \| Next Article


	Comments: webmaster@ams.org © Copyright 2009, American Mathematical Society Privacy Statement		Search the AMS