Stoll, Manfred,

Invariant Potential Theory in the Unit Ball of Cn / Manfred Stoll. - Cambridge : Cambridge University Press, 1994. - 1 online resource (184 pages) : digital, PDF file(s). - London Mathematical Society Lecture Note Series ; no. 199 . - London Mathematical Society Lecture Note Series ; no. 199. .

Title from publisher's bibliographic system (viewed on 16 Oct 2015).

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.

9780511526183 (ebook)

Potential theory (Mathematics)
Unit ball

QA404.7 / .S76 1994

The Institute of Mathematical Sciences, Chennai, India

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