Harmonic Bergman spaces in the unit Ball
Some basic techniques are established for the theory of harmonic Bergman space. For example, the hypergeometric functions are expressed as the integral of generating functions of Gegenbauer polynomials, so that we can obtain the precise form of the Forelli-Rudin type estimation for the power of harmonic Cauchy kernels. The Mobius transformations are shown to play a central role in the function theory in the real unit ball. The weighted Berman projections are considered in the limit case. As an application, the duality of weighted harmonic Bergman space with small exponents in the real unit ball is shown to be harmonic Bloch space.
Guangbin Ren, Universidade de Aveiro, Portugal
November 30, 2001