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-Boundedness of Marcinkiewicz Integrals along Surfaces with Variable Kernels: Another Sufficient Condition

Journal of Inequalities and Applications volume 2007, Article number: 026765 (2007) Cite this article

Abstract

We give the 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-boundedness holds. As corollaries of this result, we show that similar properties still hold for parametric Littlewood-Paley area integral and parametric functions with rough variable kernels. Some of the results are extensions of some known results.

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Authors and Affiliations

  1. School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, China

    Qingying Xue

  2. School of Science and Technology, Kwansei Gakuin University, Gakuen 2-1, Sanda, 669-1337, Japan

    Kôzô Yabuta

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  1. Qingying Xue
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  2. Kôzô Yabuta
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Correspondence to Kôzô Yabuta.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Xue, Q., Yabuta, K. -Boundedness of Marcinkiewicz Integrals along Surfaces with Variable Kernels: Another Sufficient Condition. J Inequal Appl 2007, 026765 (2007). https://doi.org/10.1155/2007/26765

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  • DOI: https://doi.org/10.1155/2007/26765

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