Boundedness and convergence for singular integrals of measures separated by Lipschitz graphs

Details Boundedness and convergence for singular integrals of measures separated by Lipschitz graphs Boundedness and convergence for singular integrals of measures separated by Lipschitz graphs

2008-04-02

arxiv.org/abs/0804.0405v2

Bull. London Math. Soc. 42 (2010), no. 1, 109-118

Mathematics

Functional Analysis

To appear in the Bulletin of the LMS

Scientific paper

We shall consider the truncated singular integral operators T_{\mu, K}^{\epsilon}f(x)=\int_{\mathbb{R}^{n}\setminus B(x,\epsilon)}K(x-y)f(y)d\mu y and related maximal operators $T_{\mu,K}^{\ast}f(x)=\underset{\epsilon >0}{\sup}| T_{\mu,K}^{\epsilon}f(x)|$. We shall prove for a large class of kernels $K$ and measures $\mu$ and $\nu$ that if $\mu$ and $\nu$ are separated by a Lipschitz graph, then $T_{\nu,K}^{\ast}:L^p(\nu)\to L^p(\mu)$ is bounded for $1

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