Marcinkiewicz integrals on product spaces
Studia Mathematica, Tome 167 (2005) no. 3, pp. 227-234
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
We prove the $L^p$ boundedness of the Marcinkiewicz
integral operators
$\mu_{\mit\Omega}$ on
${\mathbb R}^{n_1}\times\cdots\times{\mathbb R}^{n_k}$ under
the condition that ${\mit\Omega}
\in L (\log L)^{k/2}({\mathbb S}^{n_1 -1}\times\cdots\times{\mathbb S}^{n_k-1})$.
The exponent $k/2$ is the best possible.
This answers an open question posed by Y. Ding.
Mots-clés :
prove boundedness marcinkiewicz integral operators mit omega mathbb times cdots times mathbb under condition mit omega log mathbb times cdots times mathbb k exponent best possible answers question posed ding
Affiliations des auteurs :
H. Al-Qassem 1 ; A. Al-Salman 1 ; L. C. Cheng 2 ; Y. Pan 3
@article{10_4064_sm167_3_4,
author = {H. Al-Qassem and A. Al-Salman and L. C. Cheng and Y. Pan},
title = {Marcinkiewicz integrals on product spaces},
journal = {Studia Mathematica},
pages = {227--234},
publisher = {mathdoc},
volume = {167},
number = {3},
year = {2005},
doi = {10.4064/sm167-3-4},
language = {pl},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm167-3-4/}
}
TY - JOUR AU - H. Al-Qassem AU - A. Al-Salman AU - L. C. Cheng AU - Y. Pan TI - Marcinkiewicz integrals on product spaces JO - Studia Mathematica PY - 2005 SP - 227 EP - 234 VL - 167 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.4064/sm167-3-4/ DO - 10.4064/sm167-3-4 LA - pl ID - 10_4064_sm167_3_4 ER -
H. Al-Qassem; A. Al-Salman; L. C. Cheng; Y. Pan. Marcinkiewicz integrals on product spaces. Studia Mathematica, Tome 167 (2005) no. 3, pp. 227-234. doi: 10.4064/sm167-3-4
Cité par Sources :