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Invariant Potential Theory in the Unit Ball of Cn : London Mathematical Society Lecture Note Series - Manfred Stoll

Invariant Potential Theory in the Unit Ball of Cn

London Mathematical Society Lecture Note Series

Paperback

Published: 11th July 1994
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This monograph covers Poisson-Szego integrals on the ball, the Green's function for DEGREESD*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. It also contains recent results on admissible and tangential boundary limits of Green potentials, and Lp inequalities for the invariant gradient of Greens potentials. Applications of some of the results to Hp spaces, and weighted Bergman and Dirichlet spaces of invariant harmonic functions are included.

"The topics included in this book are well chosen and well presented." Walter Rudin, Bulletin of the American Mathematical Society

Notation and preliminary results
The Bergman kernel
The Laplace-Beltrami operator
Invariant harmonic and subharmonic functions
Poisson-Szego integrals
The Riesz decomposition theorem
Admissible boundary limits of Poisson integrals
Radial and admissible boundary limits of potentials
Gradient estimates and Riesz potentials
Spaces of invariant harmonic functions
References
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780521468305
ISBN-10: 0521468302
Series: London Mathematical Society Lecture Note Series
Audience: Professional
Format: Paperback
Language: English
Number Of Pages: 184
Published: 11th July 1994
Publisher: Cambridge University Press
Country of Publication: GB
Dimensions (cm): 22.86 x 15.24  x 1.27
Weight (kg): 0.27