English

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 (X,d)(X,d) 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 L2(μ)L^2(\mu) 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}
}