Convergence of Singular integrals with general measures

Details Convergence of Singular integrals with general measures Convergence of Singular integrals with general measures

2007-11-08

arxiv.org/abs/0711.1291v1

J. Eur. Math. Soc. (JEMS) 11 (2009), no. 2, 257-271

Mathematics

Classical Analysis and ODEs

to appear in J. Eur. Math. Soc

Scientific paper

We show that L^2-bounded singular integral 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.

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