A decomposition of Calderón--Zygmund type and some observations on differentiation of integrals on the infinite-dimensional torus

Abstract

In this note we will show a Calderón--Zygmund decomposition associated with a function $f\in L^1({\mathbb{T}}^{\omega })$. The idea relies on an adaptation of a more general result by J. L. Rubio de Francia in the setting of locally compact groups. Some related results about differentiation of integrals on the infinite-dimensional torus are also discussed.

15 pages, 4 figures, to appear in Potential Analysis