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
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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