Weighted Harmonic Bloch Spaces on the Ball

Abstract

We study the family of weighted harmonic Bloch spaces , on the unit ball of . We provide characterizations in terms of partial and radial derivatives and certain radial differential operators that are more compatible with reproducing kernels of harmonic Bergman-Besov spaces. We consider a class of integral operators related to harmonic Bergman projection and determine precisely when they are bounded on . We define projections from to and as a consequence obtain integral representations. We solve the Gleason problem and provide atomic decomposition for all . Finally we give an oscillatory characterization of when -1.