Pointwise multipliers from Dirichlet type spaces [formula omitted] to [formula omitted] spaces in the unit ball of [formula omitted

Abstract

In this paper, the pointwise multipliers M ( D τ , Q p ) and M ( D τ , Q p , 0 ) are characterized in the unit ball of C n for the values of τ , p in the three cases: (i) τ < n , n − 1 n < p ⩽ 1 , (ii) τ = n , n − 1 n < p ⩽ 1 , and (iii) τ > n , n − 1 n < p ⩽ 1 . In particular, the multiplier spaces M ( D τ , BMOA ) and M ( D τ , VMOA ) are discussed correspondingly for all τ, and the sharp embeddings of M ( D n , BMOA ) and M ( D n , VMOA ) in α-Bloch spaces are shown, respectively.