Spaces of Banach-Valued Holomorphic Functions in the Polydisk in Connection with Their Boundary Values

This chapter gives the description of the boundary values in the simplest terms of harmonic analysis on the torus Tⁿ. It applies a new technique based on the estimates connected with the Poisson kernel and on the use of the theory of vector multipliers. The chapter characterizes various classes of holomorphic functions by their radial and/or tangential properties. It describes the theorems related to the spaces of Banach-valued holomorphic functions and characterizations of the decomposition of the functions.