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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A note on $L^p$-bounded point evaluations for polynomials
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by Liming Yang
Proc. Amer. Math. Soc. 144 (2016), 4943-4948
DOI: https://doi.org/10.1090/proc/13119
Published electronically: April 19, 2016

Abstract:

We construct a compact nowhere dense subset $K$ of the closed unit disk $\bar {\mathbb D}$ in the complex plane $\mathbb C$ such that $R(K) = C(K)$ and bounded point evaluations for $P^t(dA | _K), ~ 1 \le t < \infty ,$ is the open unit disk $\mathbb D.$ In fact, there exists $C=C(t) > 0$ such that \[ \ \int _{\mathbb D} |p|^t dA \le C \int _K |p|^t dA, \] for $1 \le t < \infty$ and all polynomials $p.$
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Bibliographic Information
  • Liming Yang
  • Affiliation: School of Mathematics, Fudan University, Shanghai, People’s Republic of China
  • MR Author ID: 242102
  • Email: limingyang@fudan.edu.cn
  • Received by editor(s): November 18, 2015
  • Received by editor(s) in revised form: January 23, 2016
  • Published electronically: April 19, 2016
  • Communicated by: Pamela B. Gorkin
  • © Copyright 2016 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 144 (2016), 4943-4948
  • MSC (2010): Primary 47B20, 30H50; Secondary 30H99, 47B38
  • DOI: https://doi.org/10.1090/proc/13119
  • MathSciNet review: 3544541