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Proceedings of the American Mathematical Society

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

 

 

A Sobolev inequality for pluriharmonic functions


Author: Steven R. Bell
Journal: Proc. Amer. Math. Soc. 85 (1982), 350-352
MSC: Primary 32A40; Secondary 31C10
DOI: https://doi.org/10.1090/S0002-9939-1982-0656100-3
MathSciNet review: 656100
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Abstract: A Sobolev inequality is proved which implies that, on a smooth bounded domain $ D$ contained in $ {{\mathbf{C}}^n}$, the $ {L^2}$ inner product of two pluriharmonic functions is defined whenever one of them is in $ {C^\infty }(D)$ and the other is dominated by some negative power of the distance to the boundary.


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DOI: https://doi.org/10.1090/S0002-9939-1982-0656100-3
Article copyright: © Copyright 1982 American Mathematical Society