Sobolev type inequalities for general symmetric forms
Proc. Amer. Math. Soc. 128 (2000), 3675-3682
Primary 60J25, 47A75
June 7, 2000
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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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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
Received by editor(s):
February 27, 1998
Received by editor(s) in revised form:
September 21, 1998, and February 10, 1999
June 7, 2000
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.
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