Weighted Estimates for Toeplitz Operators Related to Pseudodifferential Operators

The authors establish the weighted Lp estimates for a class of pseudodifferential operators for both cases 1<p<∞ and p=1, where the weight class is bigger than the classical Muckenhoupt’s weight class. Moreover, the weighted estimates for the Toeplitz operators related to pseudodifferential operators are also obtained. As their special cases, the corresponding results for the commutators of pseudodifferential operators can be deduced