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On weighted inequalities for parametric Marcinkiewicz integrals

Journal of Inequalities and Applications volume 2006, Article number: 91541 (2006) Cite this article

Abstract

We establish a weighted boundedness of a parametric Marcinkiewicz integral operator if is allowed to be in the block space for some and satisfies a mild integrability condition. We apply this conclusion to obtain the weighted boundedness for a class of the parametric Marcinkiewicz integral operators and related to the Littlewood-Paley-function and the area integral, respectively. It is known that the condition is optimal for the boundedness of.

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Authors and Affiliations

  1. Department of Mathematics, Yarmouk University, Irbid-Jordan, Jordan

    H. M. Al-Qassem

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  1. H. M. Al-Qassem
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Correspondence to H. M. Al-Qassem.

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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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Al-Qassem, H.M. On weighted inequalities for parametric Marcinkiewicz integrals. J Inequal Appl 2006, 91541 (2006). https://doi.org/10.1155/JIA/2006/91541

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  • DOI: https://doi.org/10.1155/JIA/2006/91541

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