A note on weak convergence of singular integrals in metric spaces
Classical Analysis and ODEs
2016-10-17 v2
Abstract
We prove that in any metric space the singular integral operators {equation*} T^k_{\mu,\ve}(f)(x)=\int_{X\setminus B(x,\varepsilon)}k(x,y)f(y)d\mu (y).{equation*} converge weakly in some dense subspaces of under minimal regularity assumptions for the measures and the kernels.
Keywords
Cite
@article{arxiv.1304.3873,
title = {A note on weak convergence of singular integrals in metric spaces},
author = {Vasilis Chousionis and Mariusz Urbański},
journal= {arXiv preprint arXiv:1304.3873},
year = {2016}
}