Weighted Moser-Onofri-Beckner and Logarithmic Sobolev Inequalities

作者：Nguyen Lam; Lu Guozhen^*

来源：Journal of Geometric Analysis, 2018, 28(2): 1687-1715.

DOI：10.1007/s12220-017-9883-3

• Best constants
• Extremal functions
• Moser-Onofri-Beckner inequalities
• Logarithmic Sobolev inequalities

Motivated by recent results on the best constants and extremal functions for a family of the Caffarelli-Kohn-Nirenberg inequalities in [17, 23], we will study weighted Moser-Onofri-Beckner inequalities on the Euclidean space . We also set up sharp weighted versions of the logarithmic Sobolev inequalities together with their best constants and optimizers.

• 出版日期2018-4