On differentiation of integrals in the infinite-dimensional torus
Volume 258 / 2021
Studia Mathematica 258 (2021), 103-119
MSC: Primary 43A75; Secondary 42B25.
DOI: 10.4064/sm191001-10-2
Published online: 4 November 2020
Abstract
We answer the recently posed questions regarding the problem of differentiation of integrals for the Rubio de Francia basis $\mathcal R$ in the infinite torus $\mathbb T^\omega $. In particular, we prove that $\mathcal R$ does not differentiate $L^\infty ({\mathbb T}^\omega )$. Some remarks about differentiation in the context of arbitrary bases are also included.
