\(L^p\) continuity of projectors of weighted harmonic Bergman spaces (Q1566956)

We study spaces \(A^p(w)\) consisting of harmonic functions in \(B^n\) the unit ball in \(\mathbb{R}^n\) and belonging to \(L^p(w)\), where \(dw(x)=w(1-|x|)dx\) and \(w:(0,1] \to\mathbb{R}^+\) denotes a continuous integrable function. For weights satisfying certain Dini type conditions we construct families of projections of \(L^p(w)\) onto \(A^p(w)\). We use this to get for \(1<p <\infty\) and \({1\over p}+ {1\over p'}=1\), a duality \(A^p(w)^* =A^{p'}(w')\), where \(w'\) depends on \(p\) and \(w\).