TY - JOUR T1 - Weighted Estimates for Multivariate Hausdorff Operators JO - Analysis in Theory and Applications VL - 3 SP - 278 EP - 285 PY - 2012 DA - 2012/10 SN - 28 DO - http://doi.org/10.3969/j.issn.1672-4070.2012.03.008 UR - https://global-sci.org/intro/article_detail/ata/4563.html KW - multivariate Hausdorff operator, weighted $L^p$ space, Herz space. AB -

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.