On the best constant in the Khinchin-Kahane inequality

• Autorzy: Rafał Latała , Krzysztof Oleszkiewicz
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 60B11: Probability theory on linear topological spaces
• 46B09: Probabilistic methods in Banach space theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1994
• Tom: 109
• Numer: 1
• Strony: 101-104

Daty

wydano

1994

otrzymano

1993-11-02

poprawiono

1993-11-30

Twórcy

autor

Rafał Latała

• Department of Mathematics, Warsaw University, Banacha 2, 02-097 Warsaw, Poland

autor

Krzysztof Oleszkiewicz

• Department of Mathematics, Warsaw University Banacha 2, 02-097 Warsaw, Poland.

Bibliografia

• [1] U. Haagerup, The best constants in the Khintchine inequality, Studia Math. 70 (1982), 231-283.
• [2] J.-P. Kahane, Sur les sommes vectorielles $∑ ±u_n$, C. R. Acad. Sci. Paris 259 (1964), 2577-2580.
• [3] A. Khintchine [A. Khinchin], Über dyadische Brüche, Math. Z. 18 (1923), 109-116.
• [4] S. J. Szarek, On the best constants in the Khinchin inequality, Studia Math. 58 (1976), 197-208.
• [5] B. Tomaszewski, Two remarks on the Khintchin-Kahane inequality, Colloq. Math. 46 (1982), 283-288.
• [6] B. Tomaszewski, A simple and elementary proof of the Khintchine inequality with the best constant, Bull. Sci. Math. (2) 111 (1987), 103-109.