JournalsjemsVol. 11 , No. 2DOI 10.4171/jems/149

Convergence of singular integrals with general measures

  • Joan Verdera

    Universitat Autónoma de Barcelona, Spain
  • Pertti Mattila

    University of Helsinki, Finland
Convergence of singular integrals with general measures cover

Abstract

We show that L2L^2-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.