Vector-valued dirichlet-type functions on the unit ball of C n

Abstract

The vector-valued Dirichlet-type spaces on the unit ball of Cn is introduced. We discuss the pointwise multipliers of Dirichlet-type spaces. Sufficient conditions of the pointwise multipliers of\(D_\mu ^2 for 0 \leqslant \mu< 2 if n = 1 or D_{\mu .q}^2 for 0< \mu< 1 if n \geqslant 2\) are given. Finally, Rademacherp-type space is characterized by vector-valued sequence spaces.