Rough singular integral operators with Hardy space function kernels on a product domain

Ding, Yong

Ding, Yong

Colloquium Mathematicae, Tome 72 (1997), p. 15-23 / Harvested from The Polish Digital Mathematics Library

Résumé

In this paper we introduce atomic Hardy spaces on the product domain $S^{n - 1} \times S^{m - 1}$ and prove that rough singular integral operators with Hardy space function kernels are $L^{p}$ bounded on $ℝ^{n} \times ℝ^{m}$ . This is an extension of some well known results.

Publié le : 1997-01-01

Zbl 0881.42011

EUDML-ID : urn:eudml:doc:210475

@article{bwmeta1.element.bwnjournal-article-cmv73i1p15bwm,
     author = {Yong Ding},
     title = {Rough singular integral operators with Hardy space function kernels on a product domain},
     journal = {Colloquium Mathematicae},
     volume = {72},
     year = {1997},
     pages = {15-23},
     zbl = {0881.42011},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-cmv73i1p15bwm}
}

Ding, Yong. Rough singular integral operators with Hardy space function kernels on a product domain. Colloquium Mathematicae, Tome 72 (1997) pp. 15-23. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv73i1p15bwm/

Bibliographie

[000] [1] J. Duoandikoetxea, Multiple singular integrals and maximal functions along hypersurfaces, Ann. Inst. Fourier (Grenoble) 36 (4) (1986), 185-206. | Zbl 0568.42011

[001] [2] J. Duoandikoetxea and J. L. Rubio de Francia, Maximal and singular integral operators via Fourier transform estimates, Invent. Math. 84 (1986), 541-561. | Zbl 0568.42012

[002] [3] R. Fefferman, Singular integrals on product domains, Bull. Amer. Math. Soc. 4 (1981), 195-201. | Zbl 0466.42007

[003] [4] Y. S. Jiang and S. Z. Lu, A class of singular integral operators with rough kernel on product domains, Hokkaido Math. J. 24 (1995), 1-7.

[004] [5] D. K. Watson, The Hardy space kernel condition for rough integrals, preprint.