Convergence of Singular integrals with general measures
Classical Analysis and ODEs
2010-12-21 v1 Functional Analysis
Abstract
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.
Cite
@article{arxiv.0711.1291,
title = {Convergence of Singular integrals with general measures},
author = {P. Mattila and J. Verdera},
journal= {arXiv preprint arXiv:0711.1291},
year = {2010}
}
Comments
to appear in J. Eur. Math. Soc