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Sobolev type inequalities for general symmetric forms
Author(s):
Feng-Yu
Wang
Journal:
Proc. Amer. Math. Soc.
128
(2000),
3675-3682.
MSC (1991):
Primary 60J25, 47A75
Posted:
June 7, 2000
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Abstract:
A general version of the Sobolev type inequality, including both the classical Sobolev inequality and the logarithmic Sobolev one, is studied for general symmetric forms by using isoperimetric constants. Some necessary and sufficient conditions are presented as results. The main results are illustrated by two examples of birth-death processes.
References:
-
- [1]
- Aida, S., Musuda, T. and Shigekawa, I., Logarithmic Sobolev inequalities and exponential integrability, J. Funct. Anal. 126(1994), 83-101. MR 95m:60111
- [2]
- Chavel, I., Eigenvalues in Riemannian Geometry, New York: Academic Press, 1984. MR 86g:58140
- [3]
- Cheeger, J., A lower bound for the smallest eigenvalue of the Laplacian, Problems in Analysis, a symposium in honor of S. Bochner 195-199, Princeton U. Press, Princeton. MR 53:6645
- [4]
- Chen, M. F., From Markov Chains to Non-Equilibrium Particle Systems, Singapore: World Scientific, 1992. MR 94a:60135
- [5]
- Chen, M. F. and Wang, F. Y., Cheeger's inequalities for general symmetric forms and existence criteria for spectral gap, MSRI Preprint, 1998-024, to appear in Ann. Probab. CMP 99:07
- [6]
- Chung, F. R. F., Spectral Graph Theory, GBMS, 92, AMS, Providence, Rhode Island, 1997. MR 97k:58183
- [7]
- Gross, L., Logarithmic Sobolev inequalities, Amer. J. Math. 97(1975), 1061-1083. MR 54:8263
- [8]
- Lawler, G. F. and Sokal, A. D., Bounds on the
 spectrum for Markov chains and Markov processes: generalization of Cheeger's inequality, Trans. Amer. Math. Soc. 309(1998), 557-580. MR 89h:60105 - [9]
- Ledoux, M., Concentration of measure and logarithmic Sobolev inequalities, 1997 preprint.
- [10]
- Saloff-Coste, L., Lectures on finite Markov Chains, Lecture Notes in Math. 1665(1997), 301-413. MR 99b:60119
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Additional Information:
Feng-Yu
Wang
Affiliation:
Department of Mathematics, Beijing Normal University, Beijing 100875, People's Republic of China
Address at time of publication:
Universität Bielefeld, Fakultät für Mathematik, Postfach 100131, D-33501 Bielefeld, Germany
Email:
wangfy@bnu.edu.cn, fwang@mathematik.uni-bielefeld.de
DOI:
10.1090/S0002-9939-00-05471-X
PII:
S 0002-9939(00)05471-X
Keywords:
Sobolev inequality,
isoperimetric constant,
symmetric form
Received by editor(s):
February 27, 1998
Received by editor(s) in revised form:
September 21, 1998 and February 10, 1999
Posted:
June 7, 2000
Additional Notes:
The author's research was supported in part by the Alexander von Humboldt Foundation, NSFC(19631060), the Fok Ying-Tung Educational Foundation and the Research Foundation for Returned Overseas Chinese Scholars.
Communicated by:
Stanley Sawyer
Copyright of article:
Copyright
2000,
American Mathematical Society
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