Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 24, Tome 232 (1996), pp. 50-72
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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 $H^\infty$. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 24, Tome 232 (1996), pp. 50-72. http://geodesic.mathdoc.fr/item/ZNSL_1996_232_a3/
@article{ZNSL_1996_232_a3,
author = {S. A. Vinogradov and A. N. Petrov},
title = {The converse to the theorem on operation of analytic functions and multiplicative properties of some subclasses of the {Hardy} space~$H^\infty$},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {50--72},
year = {1996},
volume = {232},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_1996_232_a3/}
}
TY - JOUR
AU - S. A. Vinogradov
AU - A. N. Petrov
TI - The converse to the theorem on operation of analytic functions and multiplicative properties of some subclasses of the Hardy space $H^\infty$
JO - Zapiski Nauchnykh Seminarov POMI
PY - 1996
SP - 50
EP - 72
VL - 232
UR - http://geodesic.mathdoc.fr/item/ZNSL_1996_232_a3/
LA - ru
ID - ZNSL_1996_232_a3
ER -
%0 Journal Article
%A S. A. Vinogradov
%A A. N. Petrov
%T The converse to the theorem on operation of analytic functions and multiplicative properties of some subclasses of the Hardy space $H^\infty$
%J Zapiski Nauchnykh Seminarov POMI
%D 1996
%P 50-72
%V 232
%U http://geodesic.mathdoc.fr/item/ZNSL_1996_232_a3/
%G ru
%F ZNSL_1996_232_a3
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.
