ABOUT INTEGRAL OPERATORS WITH POISSON KERNELS IN HARDY-TYPE SPACES IN POLYDISC WITH MIXED NORM

Abstract

Hardy spaces play an important role in the complex analysis and its numerous applications. However, unlike a one-dimensional case, the Hardy-type spaces in a polydisc are investigated a little. In this paper, the integral representations of the classes of n-harmonic in a polydisc Un functions are received, in particular the characterization of n-harmonic functions in a polydisc which can be represented as a multiple Poisson integral from functions, measurable on a skeleton of a polydisc, from a class where 1 < pi < + ∞, is given. At the proof of the main result the general methods of the complex and functional analysis, theory of Hardy classes is used.