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Sobolev type inequalities for general symmetric forms

Author: Feng-Yu Wang
Journal: Proc. Amer. Math. Soc. 128 (2000), 3675-3682
MSC (1991): Primary 60J25, 47A75
Published electronically: June 7, 2000
MathSciNet review: 1691009
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Abstract | References | Similar Articles | Additional Information


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.

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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

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
Published electronically: 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
Article copyright: © Copyright 2000 American Mathematical Society