# [share_ebook] Invariant Potential Theory in the Unit Ball of Cn (London Mathematical Society Lecture Note Series)

#### Author: Manfred Stoll

#### Date: 1994-05-09

#### Pages: 184

#### Publisher: Cambridge University Press

#### Category: Study

#### Tag: Mathematics

Posted on 2011-10-09, by sharebookfree.

**Invariant Potential Theory in the Unit Ball of Cn (London Mathematical Society Lecture Note Series)**

Manfred Stoll | Cambridge University Press | 1994-05-09 | 184 pages | English | DJVU

This monograph covers Poisson-SzegÃ¶ integrals on the ball, the Green's function for ^D*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.

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