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

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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.
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DOI

10.4208/ata.2015.v31.n2.1

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$(L^p,L^q)$-Boundedness of Hausdorff Operators with Power Weight on Euclidean Spaces. (2017). Analysis in Theory and Applications, 31(2), 101-108. https://doi.org/10.4208/ata.2015.v31.n2.1