Sharp bounds for Hardy type operators on higher-dimensional product spaces |
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Authors: | Qianjun He Xiang Li Dunyan Yan |
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Institution: | School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China |
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Abstract: | 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]. |
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Keywords: | Hardy type operators power weight sharp bounds |
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