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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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Pseudo-uniform convexity of $H^{1}$ in several variables
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by Laurence D. Hoffmann
Proc. Amer. Math. Soc. 26 (1970), 609-614
DOI: https://doi.org/10.1090/S0002-9939-1970-0268656-5

Abstract:

A convergence theorem of D. J. Newman for the Hardy space ${H^1}$ is generalized to several complex variables. Specifically, in both ${H^1}$ of the polydisc and ${H^1}$ of the ball, weak convergence, together with convergence of norms, is shown to imply norm convergence. As in Newman’s work, approximation of ${L^1}$ by ${H^1}$ is also considered. It is shown that every function in ${L^1}$ of the torus, (or in ${L^1}$ of the boundary of the ball), has a best ${H^1}$-approximation which, in several variables, need not be unique.
References
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Bibliographic Information
  • © Copyright 1970 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 26 (1970), 609-614
  • MSC: Primary 46.30; Secondary 32.00
  • DOI: https://doi.org/10.1090/S0002-9939-1970-0268656-5
  • MathSciNet review: 0268656