Closure of Bergman and Dirichlet spaces in the Bloch norm

Abstract

The closure of the weighted Bergman and Dirichlet spaces in the Bloch norm is described in terms of a kind of Lusin area function and natural level sets. In certain special cases simpler characterizations are also offered. The results are applied in the study of interpolating Blaschke products.

Inclusion relations between harmonic Bergman-Besov and weighted Bloch spaces on the unit ball

“…Later, Ghatage and Zheng [13] characterized the closure of BMOA in the holomorphic Bloch space on the unit disk. Motivated by these, there has been numerous subject, namely to describe the closure of several subspaces of the holomorphic Bloch space in the Bloch norm, see [2,4,10,15,16,18,20,21,22]. Recently, Gögüş and Yılmaz [14] characterized the closures of holomorphic Bergman-Besov spaces in weighted holomorphic Bloch spaces.…”