Frontiers of Mathematics in China

, Volume 13, Issue 2, pp 449–457 | Cite as

Sharp weak bounds for n-dimensional fractional Hardy operators

Research Article
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Abstract

We obtain the operator norms of the n-dimensional fractional Hardy operator H α (0 < α < n) from weighted Lebesgue spaces \(L_{\left| x \right|^\rho }^p (\mathbb{R}^n )\) to weighted weak Lebesgue spaces \(L_{\left| x \right|^\beta }^{q,\infty } (\mathbb{R}^n )\).

Keywords

Sharp weak bound fractional Hardy operator Lebesgue space with power weight 

MSC

42B20 42B35 

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Notes

Acknowledgements

This work was partially supported by the NSFC-DFG (Grant No. 11761131002).

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Copyright information

© Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Laboratory of Mathematics and Complex Systems (Beijing Normal University), Ministry of Education; School of Mathematical SciencesBeijing Normal UniversityBeijingChina

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