Duality on vector-valued weighted harmonic Bergman spaces

Pérez-Esteva, Salvador

Studia Mathematica, Tome 119 (1996), p. 37-47 / Harvested from The Polish Digital Mathematics Library

Résumé

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*.

Publié le : 1996-01-01

Zbl 0854.46022

EUDML-ID : urn:eudml:doc:216262

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     author = {Salvador P\'erez-Esteva},
     title = {Duality on vector-valued weighted harmonic Bergman spaces},
     journal = {Studia Mathematica},
     volume = {119},
     year = {1996},
     pages = {37-47},
     zbl = {0854.46022},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv118i1p37bwm}
}

Pérez-Esteva, Salvador. Duality on vector-valued weighted harmonic Bergman spaces. Studia Mathematica, Tome 119 (1996) pp. 37-47. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv118i1p37bwm/

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