Duality on vector-valued weighted harmonic Bergman spaces

• Autorzy: Salvador Pérez-Esteva
• Języki publikacji: EN

Abstrakty

EN

We study the duals of the spaces $A^{pα}(X)$ of harmonic functions in the unit ball of $ℝ^n$ with values in a Banach space X, belonging to the Bochner $L^p$ space with weight $(1-|x|)^α$, denoted by $L^{pα}(X)$. For 0 < α < p-1 we construct continuous projections onto $A^{pα}(X)$ providing a decomposition $L^{pα}(X) = A^{pα}(X) + M^{pα}(X)$. We discuss the conditions on p, α and X for which $A^{pα}(X)* = A^{qα}(X*)$ and $M^{pα}(X)* = M^{qα}(X*)$, 1/p+1/q = 1. The last equality is equivalent to the Radon-Nikodým property of X*.

Kategorie tematyczne

• 46E15: Banach spaces of continuous, differentiable or analytic functions
• 46E40: Spaces of vector- and operator-valued functions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1996
• Tom: 118
• Numer: 1
• Strony: 37-47

Daty

wydano

1996

otrzymano

1995-01-24

poprawiono

1995-08-28

Twórcy

autor

Salvador Pérez-Esteva

• Instituto de Matemáticas, Universidad Nacional Autónoma de México, México 04510 D.F., México

Bibliografia

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