Stability of Khintchine inequalities with optimal constants between the second and the $p$-th moment for $p\ge 3$

Abstract

We give a strengthening of the classical Khintchine inequality between the second and the $p$-th moment for $p\ge 3$ with optimal constant by adding a deficit depending on the vector of coefficients of the Rademacher sum.

arXiv commentThe statement of Theorem 2 is noticeably improved compared to the previous version by slight modification of the proof (observing the identity (10))