Open Access

On weighted inequalities for parametric Marcinkiewicz integrals

Journal of Inequalities and Applications20062006:91541

DOI: 10.1155/JIA/2006/91541

Received: 25 February 2005

Accepted: 3 July 2005

Published: 20 March 2006


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 .


Authors’ Affiliations

Department of Mathematics, Yarmouk University


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© H.M. Al-Qassem. 2006

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