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Harmonic extensions of distributions

✍ Scribed by Josefina Alvarez; Martha Guzmán–Partida; Salvador Pérez–Esteva

Publisher
John Wiley and Sons
Year
2007
Tongue
English
Weight
279 KB
Volume
280
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

We obtain harmonic extensions to the upper half space of distributions in the weighted space w^n +1^D ′, which is the optimal space of tempered distributions S ′‐convolvable with the classical Euclidean version of the Poisson kernel. We also characterize the class of harmonic functions in the upper half space with boundary values in w^n +1^D ′, extending in this way results of P. Sjögren. Some facts concerning harmonic extensions of distributions in D ′, 1 < p ≤ ∞, are also approached in this paper, as well as natural relations among these spaces and the weighted space w^n +1^D ′. We can also obtain n ‐harmonic extensions of appropriate weighted integrable distributions associated to a natural product domain version of the Poisson kernel. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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