Weighted norm inequalities for pseudo-differential operators and their commutators

Abstract

This paper is dedicated to study weighted $L^p$ inequalities for pseudo-differential operators with amplitudes and their commutators by using the new class of weights A_p^\vc and the new BMO function space BMO_\vc which are larger than the Muckenhoupt class of weights $A_p$ and classical BMO space BMO, respectively. The obtained results therefore improve substantially some well-known results.Comment: correct some errors in the first versio