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2010 Boundedness of the Marcinkiewicz integrals with rough kernel associated to surfaces
Yong Ding, Qingying Xue, Kôzô Yabuta
Tohoku Math. J. (2) 62(2): 233-262 (2010). DOI: 10.2748/tmj/1277298647

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.

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Yong Ding. Qingying Xue. Kôzô Yabuta. "Boundedness of the Marcinkiewicz integrals with rough kernel associated to surfaces." Tohoku Math. J. (2) 62 (2) 233 - 262, 2010. https://doi.org/10.2748/tmj/1277298647

Information

Published: 2010
First available in Project Euclid: 23 June 2010

zbMATH: 1200.42008
MathSciNet: MR2663455
Digital Object Identifier: 10.2748/tmj/1277298647

Subjects:
Primary: 42B25
Secondary: 47G10

Rights: Copyright © 2010 Tohoku University

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Vol.62 • No. 2 • 2010
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