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Proceedings of the American Mathematical Society

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

 

 

Integrability of superharmonic functions and subharmonic functions


Author: Hiroaki Aikawa
Journal: Proc. Amer. Math. Soc. 120 (1994), 109-117
MSC: Primary 31B05
DOI: https://doi.org/10.1090/S0002-9939-1994-1169019-7
MathSciNet review: 1169019
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Abstract: We apply the coarea formula to obtain integrability of superharmonic functions and nonintegrability of subharmonic functions. The results involve the Green function. For a certain domain, say Lipschitz domain, we estimate the Green function and restate the results in terms of the distance from the boundary.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1994-1169019-7
Keywords: Superharmonic function, subharmonic function, Green function, coarea formula
Article copyright: © Copyright 1994 American Mathematical Society