The weighted \(L^ p\)-boundedness of product-type pseudodifferential operators
The author considers non-regular simple and double symbols satisfying estimates of \(S^ 0_{1,\delta}\)-type, and gives new conditions on the smoothness of the symbols, which are sufficient for the unweighted \(L^ p\)-boundedness of the associated pseudodifferential operators. The above conditions are shown to be sufficient for the boundedness on \(L^ r(w)\), where \(r\geq p\) and w is an \(A^{r/p}\)-weight of Muckenhoupt, thus filling the gap between the sufficient conditions for the unweighted \(L^ p\)-boundedness and those for the weighted \(L^ p\)-boundedness. These results are generalized to pseudodifferential operators on product domains. The proof uses paradifferential operators, the maximal inequality, and the estimate of the kernels.
scientific article; zbMATH DE number 4107326
scientific article