The weighted L^p-boundedness of product-type pseudodifferential operators

In this paper we consider non-regular simple symbols and double symbols satisfying estimates of product type, and give some sufficient conditions for the associated pseudodifferential operators to be bounded on weighted L^p-spaces, where the weights considered here are the A^q-weights of product type. In this paper we fill in the gap between the sufficient conditions for the unweighted L^p-boundedness and weighted L^p-boundedness. Some of the results are new even for the unweighted L^p-boundedness for symbols satisfying classical estimates.