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On optimal bound of Foschi’s quadratic functional in higher-dimensional spheres

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Abstract

In proving his theorem on global maximizers for the sphere adjoint Fourier restriction inequality, D. Foschi studied some quadratic functional and determined its optimal bound. In this note we extend to higher-dimensional spheres his results on this quadratic functional.

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Acknowledgements

Research of the authors is partially supported by the Provincial HEI and NSF Grants of Jiangsu (Nos. 17KJD110005 and BK20180725) and the National NSF Grant of China (No. 11801274). The authors would like to thank sincerely Professor Yan Xu for support and encouragements and to thank the anonymous referee for a detailed report.

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  1. School of Mathematical Sciences, Nanjing Normal University, Nanjing, 210023, People’s Republic of China

    Shirong Chen & Yi C. Huang

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  1. Shirong Chen
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  2. Yi C. Huang
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Correspondence to Yi C. Huang.

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Chen, S., Huang, Y.C. On optimal bound of Foschi’s quadratic functional in higher-dimensional spheres. Annali di Matematica 200, 2589–2595 (2021). https://doi.org/10.1007/s10231-021-01092-8

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  • DOI: https://doi.org/10.1007/s10231-021-01092-8

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