Gleason’s problem for harmonic mixed norm spaces in bounded star-shaped domains

Abstract

We solve Gleason’s problem for harmonic mixed norm spaces \(B^{p,q}_\alpha (\Omega ),\) where \(p,q \ge 1, \alpha >0,\) on bounded star-shaped domains in \({\mathbb {R}}^n,\) in a slightly more general form than the standard one, specifically for higher-order derivatives. The approach here is functional analytic, in particular, we first discuss the boundedness of certain integral operators, and then we prove that Gleason’s problem is solvable on harmonic mixed norm spaces \(B^{p,q}_\alpha (\Omega ).\)