Certain classes of integral operators associated with the hardy space of analytic functions

Abstract

This paper is motivated by several recent works studying the mappings of various subclasses of analytic functions by means of certain families of integral operators. The present authors investigate conditions under which some of these integral operators would map starlike and convex functions into the Hardy space H ρ(0 < ρ ≤ ∞) of analytic functions. Some of the main results presented here are also shown to be applicable to certain generalized hypergeometric functions.