Divergence of general operators on sets of measure zero

Volume 121 / 2010

G. A. Karagulyan 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.

Authors

  • G. A. KaragulyanInstitute of Mathematics of Armenian National Academy of Sciences
    Baghramian Ave. 24b
    0019 Yerevan, Armenia
    e-mail

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