Compactness of commutators of pseudo-differential operators with smooth symbols on weighted Lebesgue spaces

摘要

In this paper, we obtain the compactness of commutators of pseudo-differential operators with smooth symbols on weighted L-p spaces where the weight functions belong to a class of new weights which includes the classical Muckenhoupt weights and the results are new even on weighted L-p spaces where the weight functions belong to Muckenhoupt weights. In addition, a strong sufficient condition for compactness in new weighted L-p(1 < p < infinity) spaces is given, which has interest in its own right.