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  • Research Article
  • Open Access

On weighted inequalities for parametric Marcinkiewicz integrals

Journal of Inequalities and Applications20062006:91541

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

  • Received: 25 February 2005
  • Accepted: 3 July 2005
  • Published:

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 .

Keywords

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

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Authors’ Affiliations

(1)
Department of Mathematics, Yarmouk University, Irbid-Jordan, Jordan

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