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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A Carleson measure theorem for Bergman spaces


Author: William W. Hastings
Journal: Proc. Amer. Math. Soc. 52 (1975), 237-241
MSC: Primary 46E15; Secondary 30A78, 32A30
MathSciNet review: 0374886
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Abstract: Let $ \mu $ be a finite, positive measure on $ {U^n}$, the unit polydisc in $ {{\mathbf{C}}^n}$, and let $ {\sigma _n}$ be $ 2n$-dimensional Lebesgue volume measure on $ {U^n}$. For $ 1 \leqslant p \leqslant q < \infty $ a necessary and sufficient condition on $ \mu $ is given in order that $ \{ \int {_{{U^n}}{f^q}(z)d\mu (z){\} ^{1/q}} \leqslant } C\{ \int {_{{U^n}}{f^p}(z)d{\sigma _n}(z){\} ^{1/p}}} $ for every positive $ n$-subharmonic function $ f$ on $ {U^n}$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1975-0374886-9
PII: S 0002-9939(1975)0374886-9
Keywords: Bergman spaces, $ n$-subharmonic function, finite positive measure
Article copyright: © Copyright 1975 American Mathematical Society