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Proceedings of the American Mathematical Society
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: 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
Email: haikawa@math.shimane-u.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9939-99-04991-6
PII: S 0002-9939(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