Integral-type operators from iterated logarithmic Bloch spaces to Zygmund-type spaces

Abstract

Let H ( B ) denote the space of all holomorphic functions on the unit ball B of C n and R h ( z ) = ∑ j = 1 n z j ∂ h ∂ z j ( z ) the radial derivative of h. In this paper we study the boundedness and compactness of the following integral operator: T g ( f ) ( z ) = ∫ 0 1 f ( tz ) R g ( tz ) dt t , f ∈ H ( B ) , z ∈ B , from iterated logarithmic Bloch spaces to Zygmund-type spaces.