Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



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 $L^{p}$-integrability is proved with the estimate of $p$ in terms of the John constant.

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Additional Information

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

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