Integrability of superharmonic functions and subharmonic functions

Aikawa, Hiroaki

doi:10.1090/S0002-9939-1994-1169019-7

Integrability of superharmonic functions and subharmonic functions
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Proc. Amer. Math. Soc. 120 (1994), 109-117 Request permission

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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Note on the integrability of superharmonic functions

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