Frontiers of Mathematics in China >

2012 , Vol. 7 >Issue 5: 857 - 872

DOI: https://doi.org/10.1007/s11464-012-0237-y

RESEARCH ARTICLE

Rough Marcinkiewicz integrals along certain smooth curves

  • Bolin MA 1 ,
  • Huoxiong WU , 2 ,
  • Xiating ZHAO 2,3
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  • 1. College of Mathematics and Information Engineering, Jiaxing University, Jiaxing 314001, China
  • 2. School of Mathematical Sciences, Xiamen University, Xiamen 361005, China
  • 3. Third Middle-School of Zhuhai City, Zhuhai 519000, China

Received date: 05 Oct 2010

Accepted date: 28 Jul 2012

Published date: 01 Oct 2012

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg
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Abstract

This paper is devoted to the study of the multiple-parameter rough Marcinkiewicz integral operators associated with certain smooth curves. It is shown that the Grafakos-Stefanov type size condition Fα (Sm-1 × Sn-1) of the kernel implies the Lp-boundedness of these Marcinkiewicz integral operators for some α>1/2 and 1+12α<p<1+2α, which is an essential improvement of certain previous results.

Key words： Marcinkiewicz integral; rough kernel; smooth curve; LittlewoodPaley theory; Fourier transform estimate

Cite this article

Bolin MA , Huoxiong WU , Xiating ZHAO . Rough Marcinkiewicz integrals along certain smooth curves[J]. Frontiers of Mathematics in China, 2012 , 7(5) : 857 -872 . DOI: 10.1007/s11464-012-0237-y

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