Weighted extrapolation in grand Morrey spaces and applications to partial differential equations (Q2418835)

The authors prove weighted extrapolation theorems for grand Morrey spaces. Then they obtain new one-weight inequalities in these spaces for harmonic analysis operators for which the \(L_{w}^{p} \) boundedness holds under the Muckenhoupt \(A_{p} \) condition for the weight \(w\). These results are then used to study regularity properties of solutions of second order partial differential operators with discontinuous coefficients.