Weighted Estimates for Multivariate Hausdorff Operators (Analysis in Theory and Applications, 2012)
In this paper, some weighted estimates for the multivariate Hausdorff operators are obtained. It is proved that the multivariate Hausdorff operators are bounded on $L^p$ spaces with power weights, which is based on the boundedness of multivariate Hausdorff operators on Herz spaces, and are bounded on weighted $L^p$ spaces with the weights satisfying the homogeneity of degree zero.
Keywords: multivariate Hausdorff operator; weighted $L^p$ space; Herz space.