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April, 2013 Poisson integrals for standard weighted Laplacians in the unit disc
J. Math. Soc. Japan 65(2): 447-486 (April, 2013). DOI: 10.2969/jmsj/06520447


In this paper a counterpart of the classical Poisson integral formula is found for a class of standard weighted Laplace differential operators in the unit disc. In the process the corresponding Dirichlet boundary value problem is solved for arbitrary distributional boundary data. Boundary limits and representations of the associated solutions are studied within a framework of homogeneous Banach spaces. Special emphasis is put on the so-called relative completion of a homogeneous Banach space.


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Anders OLOFSSON. Jens WITTSTEN. "Poisson integrals for standard weighted Laplacians in the unit disc." J. Math. Soc. Japan 65 (2) 447 - 486, April, 2013.


Published: April, 2013
First available in Project Euclid: 25 April 2013

zbMATH: 1272.31002
MathSciNet: MR3055593
Digital Object Identifier: 10.2969/jmsj/06520447

Primary: 31A05
Secondary: 35J25

Keywords: Fatou theorem , homogeneous Banach space , Poisson integral , Poisson kernel , relative completion , weighted Laplace operator

Rights: Copyright © 2013 Mathematical Society of Japan

Vol.65 • No. 2 • April, 2013
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