Volume 31, Issue 2
$(L^p,L^q)$-Boundedness of Hausdorff Operators with Power Weight on Euclidean Spaces

G. L. Gao & A. Hussain

Anal. Theory Appl., 31 (2015), pp. 101-108.

Published online: 2017-04

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  • Abstract

In this paper, we prove the $(L^p, L^q)$-boundedness of (fractional) Hausdorff operators with power weight on Euclidean spaces. As special cases, we can obtain some well known results about Hardy operators.

  • Keywords

Hausdorff operator, Hardy operator, Cesàro operator, Young's inequality.

  • AMS Subject Headings

42B99, 46E30, 47B38

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{ATA-31-101, author = {}, title = {$(L^p,L^q)$-Boundedness of Hausdorff Operators with Power Weight on Euclidean Spaces}, journal = {Analysis in Theory and Applications}, year = {2017}, volume = {31}, number = {2}, pages = {101--108}, abstract = {

In this paper, we prove the $(L^p, L^q)$-boundedness of (fractional) Hausdorff operators with power weight on Euclidean spaces. As special cases, we can obtain some well known results about Hardy operators.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.2015.v31.n2.1}, url = {http://global-sci.org/intro/article_detail/ata/4626.html} }
TY - JOUR T1 - $(L^p,L^q)$-Boundedness of Hausdorff Operators with Power Weight on Euclidean Spaces JO - Analysis in Theory and Applications VL - 2 SP - 101 EP - 108 PY - 2017 DA - 2017/04 SN - 31 DO - http://doi.org/10.4208/ata.2015.v31.n2.1 UR - https://global-sci.org/intro/article_detail/ata/4626.html KW - Hausdorff operator, Hardy operator, Cesàro operator, Young's inequality. AB -

In this paper, we prove the $(L^p, L^q)$-boundedness of (fractional) Hausdorff operators with power weight on Euclidean spaces. As special cases, we can obtain some well known results about Hardy operators.

G. L. Gao & A. Hussain. (1970). $(L^p,L^q)$-Boundedness of Hausdorff Operators with Power Weight on Euclidean Spaces. Analysis in Theory and Applications. 31 (2). 101-108. doi:10.4208/ata.2015.v31.n2.1
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