Dimensional variance inequalities of Brascamp-Lieb type and a local approach to dimensional Prekopa's theorem

作者：Van Hoang Nguyen^*

来源：Journal of Functional Analysis, 2014, 266(2): 931-955.

DOI：10.1016/j.jfa.2013.11.003

• Dimensional variance inequalities
• Brascamp-Lieb type inequalities
• Sharp weighted Poincare inequalities
• Convex measures
• L-2-method

We give a new approach, inspired by Hormander's L-2-method, to weighted variance inequalities which extend results obtained by Bobkov and Ledoux. It provides in particular a local proof of the dimensional functional forms of the Brunn-Minkowski inequalities. We also present several applications of these variance inequalities, including reverse Holder inequalities for convex functions, weighted Brascamp-Lieb inequalities and sharp weighted Poincare inequalities for generalized Cauchy measures.

• 出版日期2014-1-15