Compactness of families of convolution operators with respect to convergence almost everywhere

Sergey Kostyukovsky, Alexander Olevskii

Research output: Contribution to journalArticlepeer-review

Abstract

For a given sequence of measures μn on the circle T weakly convergent to the Dirac measure, we ask, is it possible to extract a subsequence n(j) such that for any f in the space L1(L2,L) the convolutions f * μn(j) converge to f almost everywhere. We show that it is crucial whether the measures are absolutely continuous, discrete or singular (non-atomic).

Original languageEnglish
Pages (from-to)755-766
Number of pages12
JournalReal Analysis Exchange
Volume30
Issue number2
StatePublished - 2004

Keywords

  • Almost everywhere convergence
  • Convolutions

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