Integration and Differentiation in Hardy Growth Spaces

Abstract

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