Convergence of singular integrals with general measures

Mattila, Pertti, and Verdera, Joan. "Convergence of singular integrals with general measures." Journal of the European Mathematical Society 011.2 (2009): 257-271. <http://eudml.org/doc/277670>.

@article{Mattila2009,
abstract = {We show that $L^2$-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.},
author = {Mattila, Pertti, Verdera, Joan},
journal = {Journal of the European Mathematical Society},
keywords = {singular integrals; principal values; martingales; singular integrals; principal values; martingales},
language = {eng},
number = {2},
pages = {257-271},
publisher = {European Mathematical Society Publishing House},
title = {Convergence of singular integrals with general measures},
url = {http://eudml.org/doc/277670},
volume = {011},
year = {2009},
}

TY - JOUR
AU - Mattila, Pertti
AU - Verdera, Joan
TI - Convergence of singular integrals with general measures
JO - Journal of the European Mathematical Society
PY - 2009
PB - European Mathematical Society Publishing House
VL - 011
IS - 2
SP - 257
EP - 271
AB - We show that $L^2$-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.
LA - eng
KW - singular integrals; principal values; martingales; singular integrals; principal values; martingales
UR - http://eudml.org/doc/277670
ER -