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

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

1999-03-29

arxiv.org/abs/math/9903165v2

Mathematics

Classical Analysis and ODEs

28 pages, no figures, to appear Indiana Math J., final version

Scientific paper

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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