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

Abstract

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 $$L^{p}(1<p<\infty )$$ spaces is given, which has interest in its own right.