Hardy Spaces on Products of Halfplanes and Prediction of Homogeneous Random Fields

Abstract

Using the fractional linear map from the unit disk onto the upper halfplane we transfer some facts about Hardy spaces on polydisks to Hardy spaces on products of halfplanes. The results are applied to the prediction theory of homogeneous random fields on ${\mathbb{R}}^n$. In particular, we give a characterization of regular and weakly (strongly) commutative $L^2(\mu )$ spaces.