v2
https://www.raco.cat/index.php/CollectaneaMathematica/article/view/56491
2014-03-14T10:41:09Z
Collectanea Mathematica
2000: Vol.: 51 Núm.: 1; 49-58
$L^p$ continuity of projectors of weighted harmonic Bergman spaces
Blasco, Óscar
Pérez-Esteva, Salvador
2000-01-11 00:00:00
url:https://www.raco.cat/index.php/CollectaneaMathematica/article/view/56491
eng
In this paper 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 $dw(x)=w(1-\vert x\vert)dx$ and $w:(0,1]\rightarrow\mathbb{R}^+$ will denote 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 $\frac{1}{p} + \frac{1}{p'} =1$, a duality $A^p(w)^\ast=A^{p'}(w')$, where $w'$ depends on $p$ and $w$.