Invariant Potential Theory in the Unit Ball of Cn (London - download pdf or read online

By Manfred Stoll

ISBN-10: 0511526180

ISBN-13: 9780511526183

ISBN-10: 0521468302

ISBN-13: 9780521468305

This monograph offers an advent and a survey of modern leads to power concept with appreciate to the Laplace–Beltrami operator D in numerous advanced variables, with unique emphasis at the unit ball in Cn. themes coated comprise Poisson–Szegö integrals at the ball, the Green's functionality for D and the Riesz decomposition theorem for invariant subharmonic services. The extension to the ball of the classical Fatou theorem on non-tangible limits of Poisson integrals, and Littlewood's theorem at the life of radial limits of subharmonic capabilities are coated intimately. The monograph additionally comprises fresh effects on admissible and tangential boundary limits of eco-friendly potentials, and Lp inequalities for the invariant gradient of eco-friendly potentials. functions of a few of the implications to Hp areas, and weighted Bergman and Dirichlet areas of invariant harmonic capabilities are incorporated. The notes are self-contained, and may be obtainable to an individual with a few easy wisdom of a number of advanced variables.

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

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