An estimate for the composition of rough singular integral operators
Canadian mathematical bulletin, Tome 64 (2021) no. 4, pp. 911-922
Voir la notice de l'article provenant de la source Cambridge
Let $\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.
Mots-clés :
Rough singular integral operator, composite operator, weak type endpoint estimate
Tao, Xiangxing; Hu, Guoen. An estimate for the composition of rough singular integral operators. Canadian mathematical bulletin, Tome 64 (2021) no. 4, pp. 911-922. doi: 10.4153/S0008439520000946
@article{10_4153_S0008439520000946,
author = {Tao, Xiangxing and Hu, Guoen},
title = {An estimate for the composition of rough singular integral operators},
journal = {Canadian mathematical bulletin},
pages = {911--922},
year = {2021},
volume = {64},
number = {4},
doi = {10.4153/S0008439520000946},
url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008439520000946/}
}
TY - JOUR AU - Tao, Xiangxing AU - Hu, Guoen TI - An estimate for the composition of rough singular integral operators JO - Canadian mathematical bulletin PY - 2021 SP - 911 EP - 922 VL - 64 IS - 4 UR - http://geodesic.mathdoc.fr/articles/10.4153/S0008439520000946/ DO - 10.4153/S0008439520000946 ID - 10_4153_S0008439520000946 ER -
%0 Journal Article %A Tao, Xiangxing %A Hu, Guoen %T An estimate for the composition of rough singular integral operators %J Canadian mathematical bulletin %D 2021 %P 911-922 %V 64 %N 4 %U http://geodesic.mathdoc.fr/articles/10.4153/S0008439520000946/ %R 10.4153/S0008439520000946 %F 10_4153_S0008439520000946
Cité par Sources :