Journal of Inequalities and Applications
Volume 2006 (2006), Article ID 91541, 17 pages
On weighted inequalities for parametric Marcinkiewicz integrals
Department of Mathematics, Yarmouk University, Irbid-Jordan, Jordan
Received 25 February 2005; Revised 30 May 2005; Accepted 3 July 2005
Copyright © 2006 H. M. Al-Qassem. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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 .