Divergence of general operators on sets of measure zero
Volume 121 / 2010
Colloquium Mathematicum 121 (2010), 113-119
MSC: Primary 42A20
DOI: 10.4064/cm121-1-10
Abstract
We consider sequences of linear operators $U_n$ with a localization property. It is proved that for any set $E$ of measure zero there exists a set $G$ for which $U_n{\mathbb I}_G(x)$ diverges at each point $x\in E$. This result is a generalization of analogous theorems known for the Fourier sum operators with respect to different orthogonal systems.
