Integrability of superharmonic functions

in a John domain

Author:
Hiroaki Aikawa

Journal:
Proc. Amer. Math. Soc. **128** (2000), 195-201

MSC (1991):
Primary 31B05

Published electronically:
May 27, 1999

MathSciNet review:
1622765

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Abstract | References | Similar Articles | Additional Information

Abstract: The integrability of positive superharmonic functions on a bounded fat John domain is established. No exterior conditions are assumed. For a general bounded John domain the -integrability is proved with the estimate of in terms of the John constant.

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Additional Information

**Hiroaki Aikawa**

Affiliation:
Department of Mathematics, Shimane University, Matsue 690-8504, Japan

Email:
haikawa@math.shimane-u.ac.jp

DOI:
http://dx.doi.org/10.1090/S0002-9939-99-04991-6

Received by editor(s):
March 17, 1998

Published electronically:
May 27, 1999

Additional Notes:
This work was supported in part by Grant-in-Aid for Scientific Research (B) (No. 09440062), Japanese Ministry of Education, Science and Culture.

Communicated by:
Albert Baernstein II

Article copyright:
© Copyright 1999
American Mathematical Society