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https://static-content.springer.com/image/art%3A10.1155%2F2007%2F26765/MediaObjects/13660_2006_Article_1687_IEq1_HTML.gif -Boundedness of Marcinkiewicz Integrals along Surfaces with Variable Kernels: Another Sufficient Condition

Journal of Inequalities and Applications20072007:026765

DOI: 10.1155/2007/26765

Received: 18 December 2006

Accepted: 23 April 2007

Published: 6 June 2007

Abstract

We give the https://static-content.springer.com/image/art%3A10.1155%2F2007%2F26765/MediaObjects/13660_2006_Article_1687_IEq2_HTML.gif estimates for the Marcinkiewicz integral with rough variable kernels associated to surfaces. More precisely, we give some other sufficient conditions which are different from the conditions known before to warrant that the https://static-content.springer.com/image/art%3A10.1155%2F2007%2F26765/MediaObjects/13660_2006_Article_1687_IEq3_HTML.gif -boundedness holds. As corollaries of this result, we show that similar properties still hold for parametric Littlewood-Paley area integral and parametric https://static-content.springer.com/image/art%3A10.1155%2F2007%2F26765/MediaObjects/13660_2006_Article_1687_IEq4_HTML.gif functions with rough variable kernels. Some of the results are extensions of some known results.

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Authors’ Affiliations

(1)
School of Mathematical Sciences, Beijing Normal University
(2)
School of Science and Technology, Kwansei Gakuin University

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Copyright

© Q. Xue and K. Yabuta 2007

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.