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

Abstract

We investigate a class of fractional Hardy type operators {\mathcal{H}}_{{\beta }_1,{\beta }_2,\dots ,{\beta }_m} defined on higher-dimensional product spaces {ℝ}^{n_1}\times {ℝ}^{n_2}\times \cdots \times {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].

Key words： Hardy type operators; power weight; sharp bounds

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