EXTENDED CESARO OPERATORS BETWEEN MIXED-NORMSPACES AND BLOCH-TYPE SPACES IN THE UNIT BALL

摘要

This paper studies the boundedness and compactness of the following, so called, extended Cesaro operator T_gf(z)= f_0~1f(tz)~Rg(tz)dt/z ,z∈B between the mixed-norm space H (p, q, co) and the Bloch-type space B_μ (or the little Bloch-type space B_(μ,0)) of holomorphic functions on the unit ball B in C~n. For the special (but still very general) case of the weighted Bergman space A_α~p 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 T_g :B_μ→H (p, q, ψ).