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The weak-type (1,1) of L \log L homogeneous convolution operators

Terence Tao
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Abstract

We show that a homogeneous convolution kernel on an arbitrary homogeneous group which is L \log L on the unit annulus is bounded on L^p for 1 < p < \infty and is of weak-type (1,1), generalizing the result of Seeger. The proof is in a similar spirit to that of Christ and Rubio de Francia.

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Terence Tao. 1999-09-06. The weak-type (1,1) of L \log L homogeneous convolution operators. https://arxiv.org/abs/math/9903165

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