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

Zhao, Shi Ying

doi:10.1090/S0002-9939-1992-1101993-5

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

Proc. Amer. Math. Soc. 115 (1992), 677-685

DOI: https://doi.org/10.1090/S0002-9939-1992-1101993-5

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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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