# On Bell's duality theorem for harmonic functions

Joaquín Motos; Salvador Pérez-Esteva

Studia Mathematica (1999)

- Volume: 137, Issue: 1, page 49-60
- ISSN: 0039-3223

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topMotos, Joaquín, and Pérez-Esteva, Salvador. "On Bell's duality theorem for harmonic functions." Studia Mathematica 137.1 (1999): 49-60. <http://eudml.org/doc/216674>.

@article{Motos1999,

abstract = {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.},

author = {Motos, Joaquín, Pérez-Esteva, Salvador},

journal = {Studia Mathematica},

keywords = {harmonic functions; dual space; vector-valued Sobolev spaces; Bell's duality theorem},

language = {eng},

number = {1},

pages = {49-60},

title = {On Bell's duality theorem for harmonic functions},

url = {http://eudml.org/doc/216674},

volume = {137},

year = {1999},

}

TY - JOUR

AU - Motos, Joaquín

AU - Pérez-Esteva, Salvador

TI - On Bell's duality theorem for harmonic functions

JO - Studia Mathematica

PY - 1999

VL - 137

IS - 1

SP - 49

EP - 60

AB - 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.

LA - eng

KW - harmonic functions; dual space; vector-valued Sobolev spaces; Bell's duality theorem

UR - http://eudml.org/doc/216674

ER -

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