The weak-type (1,1) of L \log L homogeneous convolution operators
Abstract
Description
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.
28 pages, no figures, to appear Indiana Math J., final version
28 pages, no figures, to appear Indiana Math J., final version