an:07116673
Zbl 07116673
N????ez-Alarc??n, Daniel; Serrano-Rodr??guez, Diana Marcela
The best constants in the multiple Khintchine inequality
EN
Linear Multilinear Algebra 67, No. 11, 2325-2344 (2019).
00440202
2019
j
46B09 46G25 60B11
Khintchine inequality; mixed \((\ell_{p/(p-1)}\ell_2)\)-Littlewood inequality; multiple Khintchine inequality
First, the authors show that the Khintchine inequality and the mixed \((\ell _{p/(p-1)}\),\(\ell _{2})\)-Littlewood inequality are equivalent, that is: one can be obtained from the other one. In this way the cotype constants \(C_{2,p}\) of \(\ell _{p}\)-spaces for \(1\leq p\leq 2\) are obtained. Among other results are estimates of the optimal constants in the multiple Khintchine inequality and the optimal constants of the multilinear mixed \((\ell _{p/(p-1)}\),\(\ell _{2})\)-Littlewood inequality.
Elhadj Dahia (Bou Sa??da)
Zbl 1431.46024