Geodesic
Marcinkiewicz integrals on product spaces
H. Al-Qassem1 ; A. Al-Salman1 ; L. C. Cheng2 ; Y. Pan3
1Department of Mathematics Yarmouk University Irbid, Jordan
2Department of Mathematics Bryn Mawr College Bryn Mawr, PA 19010, U.S.A.
3Department of Mathematics University of Pittsburgh Pittsburgh, PA 15260, U.S.A.
Studia Mathematica, Tome 167 (2005) no. 3, pp. 227-234
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

Voir la notice de l'article

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.
DOI : 10.4064/sm167-3-4
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

H. Al-Qassem  1   ; A. Al-Salman  1   ; L. C. Cheng  2   ; Y. Pan  3

1 Department of Mathematics Yarmouk University Irbid, Jordan
2 Department of Mathematics Bryn Mawr College Bryn Mawr, PA 19010, U.S.A.
3 Department of Mathematics University of Pittsburgh Pittsburgh, PA 15260, U.S.A. 
@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},
     year = {2005},
     volume = {167},
     number = {3},
     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
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  - 
%0 Journal Article
%A H. Al-Qassem
%A A. Al-Salman
%A L. C. Cheng
%A Y. Pan
%T Marcinkiewicz integrals on product spaces
%J Studia Mathematica
%D 2005
%P 227-234
%V 167
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4064/sm167-3-4/
%R 10.4064/sm167-3-4
%G pl
%F 10_4064_sm167_3_4
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 :