Multipliers and closures of Besov-type spaces in the Bloch space

Abstract

Let p > 1 and let ? be a non-negative function defined in R+. A function f ? H(D) belongs to the space Bp(?) (see [4]) if ||f||p Bp(?) = |f(0)jp + ?D |(1-|z|2) f?(z)|p ?(1-|z|2)/(1-|z|2)2 dA(z) < ?. In this paper, motivated by the works of B?koll? and Bao and G???s, under some conditions on the weight function ?, we investigate the closures CB(B ? Bp(?)) of the spaces B ? Bp(?) in the Bloch space. Moreover we prove that interpolating Blaschke products in CB(B ? Bp(?)) are multipliers of Bp(?) ? BMOA.