On the best constant in the Khinchin-Kahane inequality
Volume 109 / 1994
Studia Mathematica 109 (1994), 101-104
DOI: 10.4064/sm-109-1-101-104
Abstract
We prove that if $r_i$ is the Rademacher system of functions then $(ʃ ∥∑_{i=1}^{n} x_{i}r_{i}(t)∥^2 dt)^{1/2} ≤ √2 ʃ ∥∑_{i=1}^{n}x_{i}r_{i}(t)∥dt$ for any sequence of vectors $x_i$ in any normed linear space F.
