Convergence of singular integrals with general measures
Pertti Mattila
University of Helsinki, FinlandJoan Verdera
Universitat Autónoma de Barcelona, Spain
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Abstract
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
Pertti Mattila, Joan Verdera, Convergence of singular integrals with general measures. J. Eur. Math. Soc. 11 (2009), no. 2, pp. 257–271
DOI 10.4171/JEMS/149