Cesáro type operators on spaces of analytic functions

Abstract

In this article, we consider a two parameter family of generalized Ces?ro operators P b,c , Re (b + 1) > Re c > 0, on classical spaces of analytic functions such as Hardy (H p ), BMOA and a- Bloch space (Ba). We Prove that P b,c, Re(b+1)>Re c > 0 is bounded on H p if and only if p ?(0, ?) and on Ba if and only if a ? (1, ?) and unbounded on H ?, BMOA and Ba, a ?(0, 1]. Also we prove that ?-Cesaro operators C? is a bounded operator from the Hardy space H p to the Bergmann space Ap for p ? (0, 1). Thus, we improve some well known results of the literature.