Cesàro-type operators on Hardy, BMOA and Bloch spaces

摘要

Let Hp, p∈(0,∞), BMOA and Ba, a∈(0,∞) be the classical p-Hardy, analytic BMO (a) (bounded mean oscillation on the unit circle) and a-Bloch space on the unit disk. In this paper, we prove that the Cesàro-type operator: ea a∈(-1,∞) is bounded on Hp, p∈(0,∞) and on Ba, a∈(1,∞), but, unbounded on H, BMOA and Ba, a∈(0,1). In particular, we give an answer to the Stempak's open problem.