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On the weighted $ L^p$-integrability of nonnegative $ \mathcal{M}$-superharmonic functions


Author: Shi Ying Zhao
Journal: Proc. Amer. Math. Soc. 115 (1992), 677-685
MSC: Primary 31C05; Secondary 32F05
DOI: https://doi.org/10.1090/S0002-9939-1992-1101993-5
MathSciNet review: 1101993
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Abstract: A weighted $ {L^p}$-integrability of nonnegative $ \mathcal{M}$-superharmonic functions in the unit ball of $ {\mathbb{C}^n}$ is studied in this paper. Our result is analogous to an earlier result of Armitage (J. London Math. Soc. (2) 4 (1971), 363-373) concerning the $ {L^p}$-integrability of superharmonic functions for balls in $ {\mathbb{R}^d}$. An example is given to show the sharpness of the result. Also, the weighted $ {L^p}$-integrability of the invariant Green's function for the unit ball of $ {\mathbb{C}^n}$ is obtained.


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DOI: https://doi.org/10.1090/S0002-9939-1992-1101993-5
Keywords: $ \mathcal{M}$-superharmonic functions, unit ball of $ {\mathbb{C}^n}$, integrability
Article copyright: © Copyright 1992 American Mathematical Society

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