Duality on vector-valued weighted harmonic Bergman spaces

Salvador Pérez-Esteva

Studia Mathematica (1996)

  • Volume: 118, Issue: 1, page 37-47
  • ISSN: 0039-3223

Abstract

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We study the duals of the spaces A p α ( 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 p α ( X ) . For 0 < α < p-1 we construct continuous projections onto A p α ( X ) providing a decomposition L p α ( X ) = A p α ( X ) + M p α ( X ) . We discuss the conditions on p, α and X for which A p α ( X ) * = A q α ( X * ) and M p α ( X ) * = M q α ( X * ) , 1/p+1/q = 1. The last equality is equivalent to the Radon-Nikodým property of X*.

How to cite

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Pérez-Esteva, Salvador. "Duality on vector-valued weighted harmonic Bergman spaces." Studia Mathematica 118.1 (1996): 37-47. <http://eudml.org/doc/216262>.

@article{Pérez1996,
abstract = {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*.},
author = {Pérez-Esteva, Salvador},
journal = {Studia Mathematica},
keywords = {vector-valued weighted harmonic Bergman spaces; duals; harmonic functions; Bochner space; continuous projections; Radon-Nikodým property},
language = {eng},
number = {1},
pages = {37-47},
title = {Duality on vector-valued weighted harmonic Bergman spaces},
url = {http://eudml.org/doc/216262},
volume = {118},
year = {1996},
}

TY - JOUR
AU - Pérez-Esteva, Salvador
TI - Duality on vector-valued weighted harmonic Bergman spaces
JO - Studia Mathematica
PY - 1996
VL - 118
IS - 1
SP - 37
EP - 47
AB - 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*.
LA - eng
KW - vector-valued weighted harmonic Bergman spaces; duals; harmonic functions; Bochner space; continuous projections; Radon-Nikodým property
UR - http://eudml.org/doc/216262
ER -

References

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