Extended cesàro operators between mixed-norm spaces and bloch-type spaces in the unit ball

Abstract

This paper studies the boundedness and compactness of the following, so called, extended Cesàro operator Tg(fz) = ∫01 f(tz) Rg(tz)dt/t, z ε B. between the mixed-norm space H(p, q, ℓ) and the Bloch-type space Bμ (or the little Bloch-type space Bμ,o) of holomorphic functions on the unit ball B in Cn. For the special (but still very general) case of the weighted Bergman space Aαp the paper calculates the norm of the operator for the case p > 0 and finds some upper and lower bounds for the essential norm of the operator when p > 1. When the reciprocal function of μ is Lebesgue integrable we completely characterize the boundedness and compactness of the operator Tg: Bμ → H (p, q, ℓ).