ON A NEW PRODUCT-TYPE OPERATOR ON THE UNIT BALL

Let m E N, uj , j = 1,m, be holomorphic functions on the open unit ball B C Cn , phi be a holomorphic self-map of B, and Dl be the partial derivative operator in the l th variable lE {1,2, ... ,n}. We introduce here the following polynomial differentiation composition operator PmD,phi f := m n-ary sumation j=1 ujC phi Dlj center dot center dot center dot Dl1 f and give some necessary and sufficient conditions for the boundedness and compactness of the operator from the logarithmic Bloch spaces to weighted-type spaces of holomorphic functions on B.

Automated summary

This paper investigates the polynomial differentiation composition operator and provides necessary and sufficient conditions for the boundedness and compactness of the operator from the logarithmic Bloch spaces to weighted-type spaces of holomorphic functions on B.