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

Yong Ding

Colloquium Mathematicae (1997)

  • Volume: 73, Issue: 1, page 15-23
  • ISSN: 0010-1354

Abstract

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

How to cite

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Ding, Yong. "Rough singular integral operators with Hardy space function kernels on a product domain." Colloquium Mathematicae 73.1 (1997): 15-23. <http://eudml.org/doc/210475>.

@article{Ding1997,
abstract = {In this paper we introduce atomic Hardy spaces on the product domain $S^\{n-1\}×S^\{m-1\}$ and prove that rough singular integral operators with Hardy space function kernels are $L^p$ bounded on $ℝ^\{n\} × ℝ^\{m\}$. This is an extension of some well known results.},
author = {Ding, Yong},
journal = {Colloquium Mathematicae},
keywords = {rough kernels; -boundedness; singular integral operators on product domains},
language = {eng},
number = {1},
pages = {15-23},
title = {Rough singular integral operators with Hardy space function kernels on a product domain},
url = {http://eudml.org/doc/210475},
volume = {73},
year = {1997},
}

TY - JOUR
AU - Ding, Yong
TI - Rough singular integral operators with Hardy space function kernels on a product domain
JO - Colloquium Mathematicae
PY - 1997
VL - 73
IS - 1
SP - 15
EP - 23
AB - In this paper we introduce atomic Hardy spaces on the product domain $S^{n-1}×S^{m-1}$ and prove that rough singular integral operators with Hardy space function kernels are $L^p$ bounded on $ℝ^{n} × ℝ^{m}$. This is an extension of some well known results.
LA - eng
KW - rough kernels; -boundedness; singular integral operators on product domains
UR - http://eudml.org/doc/210475
ER -

References

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  1. [1] J. Duoandikoetxea, Multiple singular integrals and maximal functions along hypersurfaces, Ann. Inst. Fourier (Grenoble) 36 (4) (1986), 185-206. Zbl0568.42011
  2. [2] J. Duoandikoetxea and J. L. Rubio de Francia, Maximal and singular integral operators via Fourier transform estimates, Invent. Math. 84 (1986), 541-561. Zbl0568.42012
  3. [3] R. Fefferman, Singular integrals on product domains, Bull. Amer. Math. Soc. 4 (1981), 195-201. Zbl0466.42007
  4. [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. 
  5. [5] D. K. Watson, The Hardy space kernel condition for rough integrals, preprint. 

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