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For any , and any , we have
where for is taken with principal branch, and denotes the real part. We show an application of this inequality: it sharpens a well-known inequality of Beckner.
Cite this article
Paata Ivanisvili, Alexander Volberg, Poincaré inequality 3/2 on the Hamming cube. Rev. Mat. Iberoam. 36 (2020), no. 1, pp. 79–97DOI 10.4171/RMI/1122