Cesaro-type operators on Hardy spaces

Given a complex Borel measure eta is an element of M([0, 1)), we study the boundedness of the Cesaro-type operator C eta given by C eta(f)(z) = Sigma(infinity)(n=0)(integral(1)(0) t(n) d eta(t))(Sigma(n)(k=0)a(k))z(n), where f(z) = Sigma(infinity)(n=0) a(n)z(n,) 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 C-mu(H-infinity(D)). subset of BMOA whenever mu is a positive Carleson measure on [0, 1). (c) 2023 The Author. Published by Elsevier Inc.