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A PARABOLIC SINGULAR INTEGRAL OPERATOR WITH ROUGH KERNEL

Part of: Harmonic analysis in several variables

Published online by Cambridge University Press:  01 April 2008

YANPING CHEN ,
YONG DING  and
DASHAN FAN
YANPING CHEN
Affiliation:
School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China Applied Science School, University of Science and Technology, Beijing 100083, China (email: yanpingch@126.com)
YONG DING*
Affiliation:
School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, China (email: dingy@bnu.edu.cn)
DASHAN FAN
Affiliation:
Department of Mathematics, University of Wisconsin–Milwaukee, Milwaukee, WI 53201, USA Huazhong Normal University, Wuhan 430074, China (email: fan@uwm.edu)
*
✉For correspondence; e-mail: dingy@bnu.edu.cn
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Abstract

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Let Ω(y′) be an H1(Sn−1) function on the unit sphere satisfying a certain cancellation condition. We study the Lp boundedness of the singular integral operator where α≥n and ρ is a norm function which is homogeneous with respect to certain nonistropic dilation. The result in the paper substantially improves and extends some known results.

Keywords

parabolic singular integralHardy spacerough kernel

MSC classification

Secondary: 42B20: Singular and oscillatory integrals (Calderón-Zygmund, etc.) 42B25: Maximal functions, Littlewood-Paley theory
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 84 , Issue 2 , April 2008 , pp. 163 - 179
Copyright
Copyright © 2008 Australian Mathematical Society

Footnotes

The research was supported by NSF of China (Grant: 19371046 and 10571015) and SRFDP of China (Grant: 20050027025).

References

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