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
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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 $p.$References
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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