Description 
1 online resource (x, 173 pages) 
Series 
London Mathematical Society lecture note series ; 199 

London Mathematical Society lecture note series ; 199.

Contents 
Cover; Halftitle; Title; Copyright; Dedication; Contents; Introduction; 1. Notation and Preliminary Results; 1.1 Notation; 1.2 Integral Formulas on B; 1.3 Automorphisms of B; 2. The Bergman Kernel; 2.1 The Bergman Kernel; 2.2 Examples; 2.3 Properties of the Bergman Kernel; 2.4 The Bergman Metric; 3. The LaplaceBeltrami Operator; 3.1 The Invariant Laplacian; 3.2 The Invariant Laplacian for Un; 3.3 The Invariant Laplacian for B; 3.4 The Invariant Gradient; 4. Invariant Harmonic and Subharmonic Functions; 4.1 M.Subharmonic Functions; 4.2 The Invariant Convolution on B; 4.3 The Riesz Measure 

10.3 MHarmonic Bergman and Dirichlet Spaces10.4 Remarks; References; Index 
Summary 
This monograph provides an introduction and a survey of recent results in potential theory with respect to the LaplaceBeltrami operator D in several complex variables, with special emphasis on the unit ball in Cn. Topics covered include PoissonSzegö 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 nontangible 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 selfcontained, and should be accessible to anyone with some basic knowledge of several complex variables 
Notes 
On t.p. "n̳" is superscript 
Bibliography 
Includes bibliographical references (pages 164169) and index 
Notes 
Print version record 
Subject 
Potential theory (Mathematics)


Invariants.


Unit ball.


MATHEMATICS  Complex Analysis.


Invariants


Potential theory (Mathematics)


Unit ball


Potentiaaltheorie.


Teoria do potencial.


Análise matemática.


Potentiel, théorie du.


Invariants.

Form 
Electronic book

ISBN 
9781107362109 

1107362105 
