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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A Carleson measure theorem for Bergman spaces
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by William W. Hastings PDF
Proc. Amer. Math. Soc. 52 (1975), 237-241 Request permission

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
  • © Copyright 1975 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 52 (1975), 237-241
  • MSC: Primary 46E15; Secondary 30A78, 32A30
  • DOI: https://doi.org/10.1090/S0002-9939-1975-0374886-9
  • MathSciNet review: 0374886