Invariant potential theory in the unit ball of Cn̳ /

This monograph provides an introduction and a survey of recent results in potential theory with respect to the Laplace-Beltrami operator D in several complex variables, with special emphasis on the unit ball in Cn. Topics covered include Poisson-Szegö integrals on the ball, the Green's functio...

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Bibliographic Details
Author / Creator:Stoll, Manfred.
Imprint:Cambridge ; New York : Cambridge University Press, 1994.
Description:1 online resource (x, 173 pages).
Language:English
Series:London Mathematical Society lecture note series ; 199
London Mathematical Society lecture note series ; 199.
Subject:Potential theory (Mathematics)
Invariants.
Unit ball.
Potentiel, Théorie du.
Invariants.
Boule unité
MATHEMATICS -- Complex Analysis.
Invariants.
Potential theory (Mathematics)
Unit ball.
Potentiaaltheorie.
Teoria do potencial.
Análise matemática.
Potentiel, théorie du.
Invariants.
Electronic books.
Electronic books.
Format: E-Resource Book
URL for this record:http://pi.lib.uchicago.edu/1001/cat/bib/11181058
Hidden Bibliographic Details
ISBN:9781107362109
1107362105
0521468302
9780521468305
Notes:On t.p. "n̳" is superscript.
Includes bibliographical references (pages 164-169) and index.
Print version record.
Summary:This monograph provides an introduction and a survey of recent results in potential theory with respect to the Laplace-Beltrami operator D in several complex variables, with special emphasis on the unit ball in Cn. Topics covered include Poisson-Szegö integrals on the ball, the Green's function for D and the Riesz decomposition theorem for invariant subharmonic functions. The extension to the ball of the classical Fatou theorem on non-tangible limits of Poisson integrals, and Littlewood's theorem on the existence of radial limits of subharmonic functions are covered in detail. The monograph also contains recent results on admissible and tangential boundary limits of Green potentials, and Lp inequalities for the invariant gradient of Green potentials. Applications of some of the results to Hp spaces, and weighted Bergman and Dirichlet spaces of invariant harmonic functions are included. The notes are self-contained, and should be accessible to anyone with some basic knowledge of several complex variables.
Other form:Print version: Stoll, Manfred. Invariant potential theory in the unit ball of Cn̳. Cambridge ; New York : Cambridge University Press, 1994 0521468302