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

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Derivatives of Hardy functions
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by Boo Rim Choe PDF
Proc. Amer. Math. Soc. 110 (1990), 781-787 Request permission

Abstract:

Let $B$ be the open unit ball of ${C^n}$, and set $S = \partial B$. It is shown that if $\varphi \in {L^p}\left ( S \right ),\varphi > 0$, is a lower semicontinuous function on $S$ and $1/q > 1 + 1/p$, then, for a given $\varepsilon > 0$, there exists a function $f \in {H^p}\left ( B \right )$ with $f\left ( 0 \right ) = 0$ such that $\left | {{f^ * }} \right | = \varphi$ almost everywhere on $S$ and $\int _B {{{\left | {\nabla f} \right |}^q}dV < \varepsilon }$ where $V$ denotes the normalized volume measure on $B$.
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Additional Information
  • © Copyright 1990 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 110 (1990), 781-787
  • MSC: Primary 32A35
  • DOI: https://doi.org/10.1090/S0002-9939-1990-1028041-8
  • MathSciNet review: 1028041