Integral representations for Riesz systems in the unit ball and some applications

Abstract

We introduce A α p A_\alpha ^p spaces of systems of harmonic functions satisfying Cauchy-Riemann equations in R n {{\mathbf {R}}^{\mathbf {n}}} and find integral representations. Using these representations and estimates for the integral kernel we prove boundedness of the representation operator in L p {L^p} and Lipschitz classes.