On the best constant in the Khinchin-Kahane inequality

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Title

Authors ¹, ²

We prove that if

r_{i}

is the Rademacher system of functions then

{(ʃ ∥ \sum_{i = 1}^{n} x_{i} r_{i} (t) ∥^{2} d t)}^{\frac{1}{2}} \leq \sqrt 2 ʃ ∥ \sum_{i = 1}^{n} x_{i} r_{i} (t) ∥ d t

for any sequence of vectors

x_{i}

in any normed linear space F.

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