Other available formats:
Looking for an inspection copy?
This title is not currently available for inspection. However, if you are interested in the title for your course we can consider offering an inspection copy. To register your interest please contact firstname.lastname@example.org providing details of the course you are teaching.
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.Read more
- Author is acknowledged expert in this field
- First book covering this material
Not yet reviewed
Be the first to review
Review was not posted due to profanity×
- Date Published: May 1994
- format: Paperback
- isbn: 9780521468305
- length: 184 pages
- dimensions: 228 x 152 x 11 mm
- weight: 0.271kg
- availability: Available
Table of Contents
1. Notation and preliminary results
2. The Bergman kernel
3. The Laplace–Beltrami operator
4. Invariant harmonic and subharmonic functions
5. Poisson–Szegö integrals
6. The Riesz decomposition theorem
7. Admissible boundary limits of Poisson integrals
8. Radial and admissible boundary limits of potentials
9. Gradient estimates and Riesz potentials
10. Spaces of invariant harmonic functions
Sorry, this resource is locked
Please register or sign in to request access. If you are having problems accessing these resources please email email@example.comRegister Sign in
You are now leaving the Cambridge University Press website. Your eBook purchase and download will be completed by our partner www.ebooks.com. Please see the permission section of the www.ebooks.com catalogue page for details of the print & copy limits on our eBooks.Continue ×
Are you sure you want to delete your account?
This cannot be undone.
Thank you for your feedback which will help us improve our service.
If you requested a response, we will make sure to get back to you shortly.×