UID:
almahu_9948233901902882
Format:
1 online resource (x, 173 pages) :
,
digital, PDF file(s).
ISBN:
9780511526183 (ebook)
Series Statement:
London Mathematical Society lecture note series ; 199
Content:
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.
Note:
Title from publisher's bibliographic system (viewed on 05 Oct 2015).
Additional Edition:
Print version: ISBN 9780521468305
Language:
English
Subjects:
Mathematics
URL:
https://doi.org/10.1017/CBO9780511526183
