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arXiv · 1304.3873

A note on weak convergence of singular integrals in metric spaces

Vasilis Chousionis·Mariusz Urbański
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Abstract

We prove that in any metric space $(X,d)$ the singular integral operators {equation*} T^k_{μ,\ve}(f)(x)=\int_{X\setminus B(x,\varepsilon)}k(x,y)f(y)dμ(y).{equation*} converge weakly in some dense subspaces of $L^2(μ)$ under minimal regularity assumptions for the measures and the kernels.

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Vasilis Chousionis, Mariusz Urbański. 2013-04-23. A note on weak convergence of singular integrals in metric spaces. https://arxiv.org/abs/1304.3873

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