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arXiv · 1101.1734

Variation and oscillation for singular integrals with odd kernel on Lipschitz graphs

Albert Mas·Xavier Tolsa
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Abstract

We prove that, for r>2, the r-variation and oscillation for the smooth truncations of the Cauchy transform on Lipschitz graphs are bounded in L^p for 1<p finite. The analogous result holds for the n-dimensional Riesz transform on n-dimensional Lipschitz graphs, as well as for other singular integral operators with odd kernel. In particular, our results strengthen the classical theorem on the L^2 boundedness of the Cauchy transform on Lipschitz graphs by Coifman, McIntosh, and Meyer.

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Albert Mas, Xavier Tolsa. 2011-09-02. Variation and oscillation for singular integrals with odd kernel on Lipschitz graphs. https://doi.org/10.1112/plms%2Fpdr061

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