Invariant Potential Theory in the Unit Ball of Cn
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Invariant Potential Theory in the Unit Ball of Cn by Manfred Stoll
Book DescriptionThis 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 DetailsISBN: 9780521468305
(228mm x 152mm x 11mm)
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, Paperback (June 2016)» View all books by Manfred Stoll
A detailed treatment of potential theory on the real hyperbolic ball and half-space aimed at researchers and graduate students.
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