| Issue |
ESAIM: PS
Volume 23, 2019
|
|
|---|---|---|
| Page(s) | 552 - 566 | |
| DOI | https://doi.org/10.1051/ps/2018025 | |
| Published online | 09 August 2019 | |
Beckner inequalities for Moebius measures on spheres☆
1
College of Mathematics and Statistics, Shenzhen University,
518060
Shenzhen, China.
2
College of Mathematics and Statistics, Wuhan University,
430072
Hubei, China.
* Corresponding author: zhlzhang.math@whu.edu.cn
Received:
26
April
2017
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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