Weighted L boundedness of pseudodifferential operators and applications

In this paper we prove weighted norm inequalities with weights in the A classes, for pseudodifferential operators with symbols in the class matamatical equation repersented that fall outside the scope of Calderón-Zygmund theory. This is accomplished by controlling the sharp function of the pseudodifferential operator by Hardy-Littlewood type maximal functions. Our weighted norm inequalities also yield L boundedness of commutators of functions of bounded mean oscillation with a wide class of operators in OPSm mathamatical equation repersented