Geodesic
Duality on vector-valued weighted harmonic Bergman spaces
Studia Mathematica, Tome 118 (1996) no. 1, pp. 37-47
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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*. 
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     author = {Salvador P\'erez-Esteva},
     title = {Duality on vector-valued weighted harmonic {Bergman} spaces},
     journal = {Studia Mathematica},
     pages = {37--47},
     year = {1996},
     volume = {118},
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     doi = {10.4064/sm-118-1-37-47},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/sm-118-1-37-47/}
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Salvador Pérez-Esteva. Duality on vector-valued weighted harmonic Bergman spaces. Studia Mathematica, Tome 118 (1996) no. 1, pp. 37-47. doi: 10.4064/sm-118-1-37-47

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