"000111 2000 eng "
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$L^p$ continuity of projectors of weighted harmonic Bergman spaces
Blasco, Óscar
Pérez-Esteva, Salvador
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 $w$.
Universitat de Barcelona
2000-01-11 00:00:00
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https://www.raco.cat/index.php/CollectaneaMathematica/article/view/56491
Collectanea Mathematica; 2000: Vol.: 51 Núm.: 1
eng