Free Holomorphic and Maximal Functions on the Unit Ball with Growth Coverings of Strongly Pseudoconvex manifolds

Abstract

Multi-analytic operators on Fock spaces are considered. We show the Functional calculus and interpolation of noncommutative operators and transformations. We study the modeling theory for commuting and noncommuting contractive with dilations of commuting tuples. We show the theory of operators on noncommutative varieties. We discuss the free Holomorphic function on the unit ball of linear Bounded operators on Hilbert spaces. We obtain the convolution operators and maximal functions for Dunkl Transforms and weighted spaces on the unit sphere. We show the Holomorphic Hilbert space functions of slow growth on covering of Pseudoconvex domains in stein manifolds