Volume 23, 2019
|Page(s)||552 - 566|
|Published online||09 August 2019|
Beckner inequalities for Moebius measures on spheres☆
College of Mathematics and Statistics, Shenzhen University,
2 College of Mathematics and Statistics, Wuhan University, 430072 Hubei, China.
* Corresponding author: email@example.com
Accepted: 26 November 2018
In this paper, we consider the Moebius measures μxn indexed by dimension n and |x| < 1 on the unit sphere Sn−1 in ℝn (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.
Mathematics Subject Classification: 60E15 / 39B62 / 26Dxx
Key words: Moebius measures / unit spheres / Beckner inequalities / Poincaré inequalities / logarithmic Sobolev inequalities
© EDP Sciences, SMAI 2019
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