Abstract
AbstractLet
$\Omega $
be homogeneous of degree zero and have mean value zero on the unit sphere
${S}^{d-1}$
,
$T_{\Omega }$
be the convolution singular integral operator with kernel
$\frac {\Omega (x)}{|x|^d}$
. In this paper, we prove that if
$\Omega \in L\log L(S^{d-1})$
, and U is an operator which is bounded on
$L^2(\mathbb {R}^d)$
and satisfies the weak type endpoint estimate of
$L(\log L)^{\beta }$
type, then the composition operator
$UT_{\Omega }$
satisfies a weak type endpoint estimate of
$L(\log L)^{\beta +1}$
type.
Publisher
Canadian Mathematical Society
Cited by
1 articles.
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