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On weighted inequalities for parametric Marcinkiewicz integrals

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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Correspondence to H. M. Al-Qassem.

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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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Keywords

  • Integral Operator
  • Integrability Condition
  • Weighted Inequality
  • Block Space
  • Weighted Boundedness
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