Extended Cesáro operators between generalized Besov spaces and Bloch type spaces in the unit ball

Abstract

Let 𝑔 be a holomorphic of the unit ball B in the n-dimensional complex space, and denote by T_g the extended Cesáro operator with symbol g. Let 0 < p < +∞, −n − 1 < q < +∞, q > −1 and α > 0, starting with a brief introduction to well known results about Cesáro operator, we investigate the boundedness and compactness of T_g between generalized Besov space B(p, q) and 𝛼α- Bloch space ℬ^α in the unit ball, and also present some necessary and sufficient conditions.