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

Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 24, Tome 232 (1996), pp. 50-72

Résumé

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.