Geodesic
On Bell's duality theorem for harmonic functions
Studia Mathematica, Tome 137 (1999) no. 1, pp. 49-60

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/sm-137-1-49-60

Joaquín Motos 1 ;  1

1 
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Joaquín Motos;  . On Bell's duality theorem for harmonic functions. Studia Mathematica, Tome 137 (1999) no. 1, pp. 49-60. doi: 10.4064/sm-137-1-49-60

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