## Tohoku Mathematical Journal

### Boundedness of the Marcinkiewicz integrals with rough kernel associated to surfaces

#### 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

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

#### 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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