Invariant Potential Theory in the Unit Ball of Cn by Manfred Stoll
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Invariant Potential Theory in the Unit Ball of Cn
By Manfred Stoll

Invariant Potential Theory in the Unit Ball of Cn

By (author) See other recent books by Manfred Stoll
Series edited by N. J. Hitchin See other recent books by N. J. Hitchin
Format: Paperback

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Invariant Potential Theory in the Unit Ball of Cn by Manfred Stoll

Book Description

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-Szego 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.

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Book Details

ISBN: 9780521468305
ISBN-10: 0521468302
Format: Paperback
(228mm x 152mm x 11mm)
Pages: 184
Imprint: Cambridge University Press
Publisher: Cambridge University Press
Publish Date: 12-May-1994
Country of Publication: United Kingdom

Books By Author Manfred Stoll

Harmonic and Subharmonic Function Theory on the Hyperbolic Ball by Manfred Stoll Harmonic and Subharmonic Function Theory on the Hyperbolic Ball, Paperback (June 2016)

A detailed treatment of potential theory on the real hyperbolic ball and half-space aimed at researchers and graduate students.

» View all books by Manfred Stoll

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