JournalsjemsVol. 11, No. 2pp. 257–271

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
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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.

Cite this article

Joan Verdera, Pertti Mattila, Convergence of singular integrals with general measures. J. Eur. Math. Soc. 11 (2009), no. 2, pp. 257–271

DOI 10.4171/JEMS/149