Convergence of singular integrals with general measures

Pertti Mattila, Joan Verdera

Research output: Contribution to journalArticleResearchpeer-review

19 Citations (Scopus)

Abstract

We show that L2-bounded singular integrals in metric spaces with respect to general measures and kernels converge weakly. This implies a kind of average convergence almost everywhere. For measures with zero density we prove the almost everywhere existence of principal values. © European Mathematical Society 2009.
Original languageEnglish
Pages (from-to)257-271
JournalJournal of the European Mathematical Society
Volume11
Issue number2
DOIs
Publication statusPublished - 1 Jan 2009

Keywords

  • Martingales
  • Principal values
  • Singular integrals

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