TY - JOUR
T1 - Sharp stability of log-Sobolev and Moser-Onofri inequalities on the sphere
AU - Chen, Lu
AU - Lu, Guozhen
AU - Tang, Hanli
N1 - Publisher Copyright:
© 2023
PY - 2023/9/1
Y1 - 2023/9/1
N2 - In this paper, we are concerned with the stability problem for endpoint conformally invariant cases of the Sobolev inequality on the sphere Sn. Namely, we will establish the stability for Beckner's log-Sobolev inequality and Beckner's Moser-Onofri inequality on the sphere. We also prove that the sharp constant of global stability for the log-Sobolev inequality on the sphere Sn must be strictly smaller than the sharp constant of local stability for the same inequality. Furthermore, we also derive the non-existence of the global stability for Moser-Onofri inequality on the sphere Sn.
AB - In this paper, we are concerned with the stability problem for endpoint conformally invariant cases of the Sobolev inequality on the sphere Sn. Namely, we will establish the stability for Beckner's log-Sobolev inequality and Beckner's Moser-Onofri inequality on the sphere. We also prove that the sharp constant of global stability for the log-Sobolev inequality on the sphere Sn must be strictly smaller than the sharp constant of local stability for the same inequality. Furthermore, we also derive the non-existence of the global stability for Moser-Onofri inequality on the sphere Sn.
KW - Local and global stability
KW - Log Sobolev inequality on the sphere
KW - Moser-Onofri inequality
UR - https://www.scopus.com/pages/publications/85161081750
U2 - 10.1016/j.jfa.2023.110022
DO - 10.1016/j.jfa.2023.110022
M3 - Article
AN - SCOPUS:85161081750
SN - 0022-1236
VL - 285
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
IS - 5
M1 - 110022
ER -