Volume 28, Issue 3
Weighted Estimates for Multivariate Hausdorff Operators

Anal. Theory Appl., 28 (2012), pp. 278-285.

Published online: 2012-10

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• Abstract

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.

42B25, 42B35

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@Article{ATA-28-278, author = {}, title = {Weighted Estimates for Multivariate Hausdorff Operators}, journal = {Analysis in Theory and Applications}, year = {2012}, volume = {28}, number = {3}, pages = {278--285}, abstract = {

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} }
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.

Yanling Sun & Yinsheng Jiang. (1970). Weighted Estimates for Multivariate Hausdorff Operators. Analysis in Theory and Applications. 28 (3). 278-285. doi:10.3969/j.issn.1672-4070.2012.03.008
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