Harmonic extensions of distributions | Zendy

Alvarez Josefina | Zendy; Guzmán–Partida Martha | Zendy; Pérez–Esteva Salvador | Zendy

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Harmonic extensions of distributions

Author(s) -

Alvarez Josefina,

Guzmán–Partida Martha,

Pérez–Esteva Salvador

Publication year - 2007

Publication title -

mathematische nachrichten

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.913

H-Index - 50

eISSN - 1522-2616

pISSN - 0025-584X

DOI - 10.1002/mana.200510558

Subject(s) - mathematics , poisson kernel , integrable system , euclidean space , harmonic , space (punctuation) , poisson distribution , kernel (algebra) , harmonic function , mathematical analysis , pure mathematics , distribution (mathematics) , domain (mathematical analysis) , boundary (topology) , class (philosophy) , product (mathematics) , geometry , statistics , quantum mechanics , physics , linguistics , philosophy , artificial intelligence , computer science

We obtain harmonic extensions to the upper half space of distributions in the weighted space w n +1 D ′ L 1, 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 ′ L 1, extending in this way results of P. Sjögren. Some facts concerning harmonic extensions of distributions in D ′ L p, 1 < p ≤ ∞, are also approached in this paper, as well as natural relations among these spaces and the weighted space w n +1 D ′ L 1. 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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