Previous issue ·  Next issue ·  Most recent issue · All issues

Journal of Operator Theory

Volume 52, Issue 1, Summer 2004  pp. 173-184.

Weighted composition operators of spaces of functions with derivative in a Hardy space

Authors M.D. Contreras (1) and A.G. Hernandez-Diaz (2)
Author institution: (1) Departamento de Matematica Aplicada II, Escuela Superior de Ingenieros, Universidad de Sevilla, Camino de los Descubrimientos, s/n, 41092, Sevilla, Spain
(2) Departamento de Matematica Aplicada II, Escuela Superior de Ingenieros, Universidad de Sevilla, Camino de los Descubrimientos, s/n, 41092, Sevilla, Spain

Summary:  Let $\varphi$ and $\psi$ be two analytic functions defined on ${\bbb D}$ such that $\varphi ( {\bbb D}) \subseteq {\bbb D}$. The operator given by $f\mapsto \psi ( f\circ \varphi )$ is called a weighted composition operator. For each $1\leq p\leq \infty ,$ let $S_{p}$ be the space of analytic functions on ${\bbb D}$ whose derivatives belong to the Hardy space $H_{p}.$ In this paper we deal with boundedness, compactness, weak compactness, and complete continuity of weighted composition operators from $S_{p}$ into $S_{q}$ for $1\leq p,q\leq \infty$.

Contents    Full-Text PDF