L[p] continuity of projectors of weighted harmonic Bergman spaces

• Autores: Óscar Blasco de la Cruz , Salvador Pérez-Esteva
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 51, Fasc. 1, 2000, págs. 49-58
• Idioma: inglés
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• Resumen

  • 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 $w$.

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