Tohoku Mathematical Journal

Boundedness of the Marcinkiewicz integrals with rough kernel associated to surfaces

Yong Ding, Qingying Xue, and Kôzô Yabuta

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Abstract

In this paper, the authors discuss the weighted $L^p$ boundedness for the rough Marcinkiewicz integrals associated to surfaces. More precisely, the kernel of our operator lacks smoothness not only on the unit sphere, but also in the radial directions. Moreover, the surface is defined by using a differentiable function with monotonicity and some properties on the positive real line. The results given in this paper improve and extend some known results.

Article information

Source
Tohoku Math. J. (2), Volume 62, Number 2 (2010), 233-262.

Dates
First available in Project Euclid: 23 June 2010

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1277298647

Digital Object Identifier
doi:10.2748/tmj/1277298647

Mathematical Reviews number (MathSciNet)
MR2663455

Zentralblatt MATH identifier
1200.42008

Subjects
Primary: 42B25: Maximal functions, Littlewood-Paley theory
Secondary: 47G10: Integral operators [See also 45P05]

Keywords
Marcinkiewicz integrals $L^p$ boundedness weighted boundedness rough kernel

Citation

Ding, Yong; Xue, Qingying; Yabuta, Kôzô. Boundedness of the Marcinkiewicz integrals with rough kernel associated to surfaces. Tohoku Math. J. (2) 62 (2010), no. 2, 233--262. doi:10.2748/tmj/1277298647. https://projecteuclid.org/euclid.tmj/1277298647


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References

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