Weak type estimates for singular integral operators with variable kernels on the weighted Hardy spaces

Details Weak type estimates for singular integral operators with variable kernels on the weighted Hardy spaces Weak type estimates for singular integral operators with variable kernels on the weighted Hardy spaces

2011-11-18

arxiv.org/abs/1111.4269v1

Mathematics

Classical Analysis and ODEs

10 pages

Scientific paper

Let $T_\Omega$ be the singular integral operator with variable kernel
$\Omega(x,z)$. In this paper, by using the atomic decomposition theory of
weighted Hardy spaces, we will obtain the weighted weak type estimates of
$T_\Omega$ on these spaces, under some Dini type conditions imposed on the
kernel $\Omega(x,z)$. This result is new even in the unweighted case.

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