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Zapiski Nauchnykh Seminarov POMI, 1996, Volume 232, Pages 50–72
(Mi znsl3675)
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This article is cited in 1 scientific paper (total in 1 paper)
The converse to the theorem on operation of analytic functions and multiplicative properties of some subclasses of the Hardy space $H^\infty$
S. A. Vinogradov, A. N. Petrov St. Petersburg State University
Abstract:
In the note multiplicative properties of function spaces $V\cap l^p_A(w)$ are investigated. The space $V$ is defined by values of functions (for example, $C_A$, $\operatorname{Lip}_A\alpha$), $l^p_A(w)$ is the space of power series with the Taylor coefficients which are summable with the power $p$ and the weight $w$. The converse to the theorem on operation of analytic functions in such spaces, theorems on $\operatorname{mult}(V\cap l^p_A(w))$, the estimate of the Salem–Zygmund type for $l^p$-multiplier norm of random polynomials are obtained. Bibl. 10 titles.
Received: 20.11.1995
Citation:
S. A. Vinogradov, A. N. Petrov, “The converse to the theorem on operation of analytic functions and multiplicative properties of some subclasses of the Hardy space $H^\infty$”, Investigations on linear operators and function theory. Part 24, Zap. Nauchn. Sem. POMI, 232, POMI, St. Petersburg, 1996, 50–72; J. Math. Sci. (New York), 92:1 (1998), 3573–3588
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https://www.mathnet.ru/eng/znsl3675 https://www.mathnet.ru/eng/znsl/v232/p50
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Abstract page: | 156 | Full-text PDF : | 60 |
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