02348nam a22003738a 4500001001600000003000700016005001700023006001900040007001500059008004100074020002600115020003000141040002400171050002400195082001300219100002900232245007200261260005200333264005200385300005900437336002600496337002600522338003600548490006300584500007300647520103000720650003501750650001501785650001401800776003501814786001401849830006401863856004701927CR9780511526183UkCbUP20160624102257.0m|||||o||d||||||||cr||||||||||||090407s1994||||enk s ||1 0|eng|d a9780511526183 (ebook) z9780521468305 (paperback) aUkCbUPcUkCbUPerda00aQA404.7 b.S76 199400an/a2n/a1 aStoll, Manfred,eauthor.10aInvariant Potential Theory in the Unit Ball of Cn /cManfred Stoll. 1aCambridge :bCambridge University Press,c1994. 1aCambridge :bCambridge University Press,c1994. a1 online resource (184 pages) :bdigital, PDF file(s). atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier0 aLondon Mathematical Society Lecture Note Series ;vno. 199 aTitle from publisher's bibliographic system (viewed on 16 Oct 2015). aThis 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. 0aPotential theory (Mathematics) 0aInvariants 0aUnit ball08iPrint version: z9780521468305 dCambridge 0aLondon Mathematical Society Lecture Note Series ;vno. 199.40uhttp://dx.doi.org/10.1017/CBO9780511526183