Beckner inequalities for Moebius measures on spheres
ESAIM: Probability and Statistics, Tome 23 (2019), pp. 552-566

In this paper, we consider the Moebius measures μ$$$$ indexed by dimension n and |x| < 1 on the unit sphere S$$ in ℝ$$ (n ≥ 3), and provide a precise two-sided estimate on the order of the Beckner inequality constant with exponent p ∈ [1, 2) in the three parameters. As special cases for p = 1 and p tending to 2, our results cover those in Barthe et al. [Forum Math. (submitted for publication)] for n ≥ 3 and explore an interesting phenomenon.

Reçu le :
Accepté le :
DOI : 10.1051/ps/2018025
Classification : 60E15, 39B62, 26Dxx
Keywords: Moebius measures, unit spheres, Beckner inequalities, Poincaré inequalities, logarithmic Sobolev inequalities

Yao, Nian 1 ; Zhang, Zhengliang 1

1 
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     author = {Yao, Nian and Zhang, Zhengliang},
     title = {Beckner inequalities for {Moebius} measures on spheres},
     journal = {ESAIM: Probability and Statistics},
     pages = {552--566},
     year = {2019},
     publisher = {EDP Sciences},
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     doi = {10.1051/ps/2018025},
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     url = {https://www.numdam.org/articles/10.1051/ps/2018025/}
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Yao, Nian; Zhang, Zhengliang. Beckner inequalities for Moebius measures on spheres. ESAIM: Probability and Statistics, Tome 23 (2019), pp. 552-566. doi: 10.1051/ps/2018025

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