Rubio de Francia's weighted extrapolation in mixed-norm spaces and applications

Weighted extrapolation for pairs of functions in mixed-norm Banach function spaces defined on the product of quasi-metric measure spaces (X,d,& mu;)$(X, d, \mu )$ and (Y,& rho;,& nu;)$(Y, \rho , \nu )$ are derived. As special cases, we have appropriate results for mixed-norm Lebesgue, Lorentz, and Orlicz spaces. Some of the derived results are applied to get weighted extrapolation in mixed-norm grand Lebesgue spaces.