We show that -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. 257–271DOI 10.4171/JEMS/149