On the L 2 boundedness of parametric Marcinkiewicz integral operator

In this paper, we derive a multiplier formula for Hörmander's parametric Marcinkiewicz integral operator. As a consequence, we prove the optimality of the kernel size condition L ( log L ) 1 / 2 ( S n − 1 ) as well as the optimality of the Block size condition.

Saved in:
Bibliographic Details
Published in:Journal of mathematical analysis and applications 2011-03, Vol.375 (2), p.745-752
Main Author: Al-Salman, Ahmad
Format: Article
Language:English
Subjects:
Block spaces
Marcinkiewicz integrals
Parametric Marcinkiewicz integrals
Singular integrals
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this paper, we derive a multiplier formula for Hörmander's parametric Marcinkiewicz integral operator. As a consequence, we prove the optimality of the kernel size condition L ( log L ) 1 / 2 ( S n − 1 ) as well as the optimality of the Block size condition.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2010.09.062