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International Journal of Analysis
Volume 2013, Article ID 798528, 12 pages
http://dx.doi.org/10.1155/2013/798528
Research Article

New Weighted Norm Inequalities for Pseudodifferential Operators and Their Commutators

1Department of Mathematics, Ho Chi Minh City University of Pedagogy, Ho Chi Minh City 70000, Vietnam
2Department of Mathematics, Macquarie University, Sydney, NSW 2109, Australia

Received 18 August 2012; Accepted 13 November 2012

Academic Editor: Serge Nicaise

Copyright © 2013 The Anh Bui. 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.

Abstract

This paper is dedicated to study weighted inequalities for pseudodifferential operators with amplitudes and their commutators by using the new class of weights and the new BMO function space BMO which are larger than the Muckenhoupt class of weights and classical BMO space BMO, respectively. The obtained results therefore improve substantially some well-known results.