Multipliers on Dirichlet Type Spaces.

Abstract In this paper, we characterize the pointwise multiplier space M(D[sub tau], D[sub mu]) of Dirichlet type spaces in the unit ball of C[sup n] for the values of tau, mu in three cases: (i) tau < 0, mu < 0, (ii) tau < mu, (iii) tau >/- mu, tau > n, and construct two functions to show theft M(D[sub tau]) subset D[sub tau] properly if tau less than or equal to n and M(D[sub tau]) subset M(D[sub mu]) properly if tau > mu and tau > n 1. Keywords Dirichlet space, Pointwise multiplier Holomorphic function [ABSTRACT FROM AUTHOR]