Cesàro-type operators on Hardy spaces

Abstract

Given a complex Borel measure η∈M([0,1)), we study the boundedness of the Cesàro-type operator Cη given by Cη(f)(z)=∑n=0∞(∫01tndη(t))(∑k=0nak)zn, where f(z)=∑n=0∞anzn, acting on Hardy spaces, BMOA and the Bloch space B. We recover the recent results achieved for positive measures in [9]. We also solve the question that was left open in that paper and show that Cμ(H∞(D))⊂BMOA whenever μ is a positive Carleson measure on [0,1).

Topics & Concepts