Singular integral operators with rough convolution kernels

Abstract

in all dimensions, again under the assumption Q e L log L. It is conceivable that a variant of the arguments in [3] for the maximal operator could also work for the singular integral operator; in fact, in unpublished work, the authors of [3] obtained a weak type (1, 1) inequality in dimension d < 7. However their arguments if applied to the singular integral operator lead to substantial technical difficulties and no