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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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

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

First available in Project Euclid: 23 June 2010

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

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


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.

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