Anal. Theory Appl., 28 (2012), pp. 278-285.
Published online: 2012-10
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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.
}, issn = {1573-8175}, doi = {https://doi.org/10.3969/j.issn.1672-4070.2012.03.008}, url = {http://global-sci.org/intro/article_detail/ata/4563.html} }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.