Integration and differentiation operators between growth spaces

Abstract

For arbitrary radial weights $w$ and $u$, we study the integration operator between the growth spaces $H_w^{\infty }$ and $H_u^{\infty }$ on the complex plane. Also, we investigate the differentiation operator on the Hardy growth spaces $H_w^p$, $0<p<\infty$, defined on the unit disk or on the complex plane. As in the case $p=\infty$, the log-convex weights $w$ play a special role in the problems under consideration.

9 pages

References in corpus (1)

• Harmonic approximation by finite sums of moduli