L^p estimates for the maximal singular integral in terms of the singular integral
Anna Bosch Camos,
(UAB - UPV/EHU)
Miércoles 31 de octubre 2012
It was recently proved, see \cite{MOV}, that in
the case of even smooth homogeneous Calder\'on-Zygmund operators the
$L^2$ estimate of $T^{\star}$ by $T$ is equivalent to the
pointwise inequality between $T^{\star}$ and $M(T)$. We extend
this result to the corresponding $L^p$ estimate, that is, the
estimate of the $L^p$ norm of $T^{\star}f$ by a constant times the
$L^p$ norm of $Tf$ implies the pointwise inequality between
$T^{\star}$ and $M(T)$. Similar results are obtained for weighted
$L^p$, weak $L^1$ and also for odd kernels. Joint work with Joan Mateu
and Joan Orobitg.
\begin{thebilbioagraphy}}{CMM}
\bibitem[MOV]{MOV} J. Mateu, J. Orobitg, J. Verdera \emph{ Estimates
for the maximal singular integral
in terms of the singular integral:
the case of even kernels}, Annals of Mathematics 174 (2011), 1429--1483.
\end{thebibliography}