On an integral-type operator from logarithmic Bloch-type spaces to mixed-norm spaces on the unit ball

Abstract

Let H ( B ) denote the space of all holomorphic functions on the open unit ball B of C n and g ∈ H ( B ) . We characterize the boundedness and compactness of the following integral-type operator L g f ( z ) = ∫ 0 1 R f ( tz ) g ( tz ) dt t , z ∈ B , where R f is the radial derivative of function f, from logarithmic Bloch-type spaces to mixed-norm spaces on the unit ball.