On the best constant in the Khinchin-Kahane inequality

Latała, Rafał; Oleszkiewicz, Krzysztof

Studia Mathematica, Tome 108 (1994), p. 101-104 / Harvested from The Polish Digital Mathematics Library

Résumé

We prove that if $r_{i}$ is the Rademacher system of functions then ${(ʃ ∥ \sum_{i = 1}^{n} x_{i} r_{i} (t) ∥^{2} d t)}^{1 / 2} \leq \sqrt 2 ʃ ∥ \sum_{i = 1}^{n} x_{i} r_{i} (t) ∥ d t$ for any sequence of vectors $x_{i}$ in any normed linear space F.

Publié le : 1994-01-01

Zbl 0812.60010

EUDML-ID : urn:eudml:doc:216056

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     author = {Rafa\l\ Lata\l a and Krzysztof Oleszkiewicz},
     title = {On the best constant in the Khinchin-Kahane inequality},
     journal = {Studia Mathematica},
     volume = {108},
     year = {1994},
     pages = {101-104},
     zbl = {0812.60010},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv109i1p101bwm}
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Latała, Rafał; Oleszkiewicz, Krzysztof. On the best constant in the Khinchin-Kahane inequality. Studia Mathematica, Tome 108 (1994) pp. 101-104. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv109i1p101bwm/

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