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1

Duality on vector-valued weighted harmonic Bergman spaces

100%

Pérez-Esteva S.

Studia Mathematica

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1996

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tom 118

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nr 1

37-47

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*.

2

On Bell's duality theorem for harmonic functions

63%

Motos J., Pérez-Esteva S.

Studia Mathematica

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1999

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tom 137

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nr 1

49-60

EN

Define $h^∞(E)$ as the subspace of $C^∞(B̅L,E)$ consisting of all harmonic functions in B, where B is the ball in the n-dimensional Euclidean space and E is any Banach space. Consider also the space $h^{-∞}(E*)$ consisting of all harmonic E*-valued functions g such that $(1-|x|)^mf$ is bounded for some m>0. Then the dual $h^∞(E*)$ is represented by $h^{-∞}(E*)$ through $⟨f,g⟩_0= lim_{r→1}ʃ_B ⟨f(rx),g(x)⟩dx$, $f ∈ h^{-∞}(E*),g ∈ h^∞(E)$. This extends the results of S. Bell in the scalar case.

3

The Bergman projection on weighted spaces: L¹ and Herz spaces

63%

Blasco O., Pérez-Esteva S.

Studia Mathematica

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2002

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tom 150

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nr 2

151-162

EN

We find necessary and sufficient conditions on radial weights w on the unit disc so that the Bergman type projections of Forelli-Rudin are bounded on L¹(w) and in the Herz spaces $K_{p}^{q}(w)$.

Ograniczanie wyników

3 Studia Mathematica

3 Pérez-Esteva S.

1 Blasco O.

1 Motos J.

1 2002

1 1999

1 1996

Duality on vector-valued weighted harmonic Bergman spaces

On Bell's duality theorem for harmonic functions

The Bergman projection on weighted spaces: L¹ and Herz spaces