Frontiers of Mathematics in China

, Volume 13, Issue 6, pp 1341–1353 | Cite as

Sharp bounds for Hardy type operators on higher-dimensional product spaces

  • Qianjun HeEmail author
  • Xiang Li
  • Dunyan Yan
Research Article


We investigate a class of fractional Hardy type operators \({\mathscr{H}_{{\beta _1},{\beta _2}, \ldots ,{\beta _m}}}\) defined on higher-dimensional product spaces \({\mathbb{R}^{{n_1}}} \times {\mathbb{R}^{{n_2}}} \times \cdots \times {\mathbb{R}^{{n_m}}}\) and use novel methods to obtain their sharp bounds. In particular, we optimize the result due to S. M. Wang, S. Z. Lu, and D. Y. Yan [Sci. China Math., 2012, 55(12): 2469–2480].


Hardy type operators power weight sharp bounds 


42B20 42B25 


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This work was supported by the National Natural Science Foundation of China (Grant Nos. 11471309, 11561062, 11871452).


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Copyright information

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

Authors and Affiliations

  1. 1.School of Mathematical SciencesUniversity of Chinese Academy of SciencesBeijingChina

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