×

zbMATH — the first resource for mathematics

Optimal blow up rate for the constants of Khinchin type inequalities. (English) Zbl 1391.60008
Summary: We provide, among other results, the optimal blow up rate of the constants of a family of Khinchin inequalities for multiple sums.

MSC:
60B11 Probability theory on linear topological spaces
46B09 Probabilistic methods in Banach space theory
PDF BibTeX XML Cite
Full Text: DOI arXiv
References:
[1] Achour, D.; Mezrag, L., On the Cohen strongly p-summing multilinear operators, J. Math. Anal. Appl., 327, 1, 550-563, (2007) · Zbl 1121.47013
[2] Adams, R.; Fournier, J.J.F., Sobolev spaces, (2003), Academic Press, Amsterdam
[3] Albuquerque, N., Sharp generalizations of the multilinear Bohnenblust-Hille inequality, J. Funct. Anal., 266, 6, 3726-3740, (2014) · Zbl 1319.46035
[4] Cavalcante, W.; Núñez-Alarcón, D., Remarks on an inequality of Hardy and Littlewood, Quaest. Math., 39, 1101-1113, (2016)
[5] Diestel, J.; Jarchow, H.; Tonge, A., Absolutely summing operators, 43, (1995), Cambridge University Press, Cambridge Studies in Advanced Mathematics, Cambridge · Zbl 0855.47016
[6] Haagerup, U., The best constants in the Khintchine inequality, Studia Math., 70, 3, 231-283, (1981) · Zbl 0501.46015
[7] Hall, R.R., On a conjecture of Littlewood, Math. Proc. Cambridge Philos. Soc., 78, 3, 443-445, (1975) · Zbl 0325.52016
[8] Khintchine, A., Über dyadische brüche, Math. Z., 18, 1, 109-116, (1923) · JFM 49.0132.01
[9] Lata-la, R.; Oleszkiewicz, K., On the best constant in the Khinchin-kahane inequality, Studia Math., 109, 1, 101-104, (1994) · Zbl 0812.60010
[10] Mujica, J., Complex analysis in Banach spaces, (2010), Dover Publications Inc. Mineola, New York
[11] Pellegrino, D., The optimal constants of the mixed (1, ℓ2)-Littlewood inequality, J. Number Theory, 160, 11-18, (2016) · Zbl 1431.46024
[12] Pérez-García, D.; Villanueva, I., Multiple summing operators on Banach spaces, J. Math. Anal. Appl., 285, 1, 86-96, (2003) · Zbl 1044.46037
[13] Popa, D., Multiple Rademacher means and their applications, J. Math. Anal. Appl., 386, 2, 699-708, (2012) · Zbl 1233.47016
[14] Szarek, S.J., On the best constants in the Khinchin inequality, Studia Math., 58, 2, 197-208, (1976) · Zbl 0424.42014
[15] Tomaszewski, B., A simple and elementary proof of the Khintchine inequality with the best constant, Bull. Sci. Math. (2), 111, 1, 103-109, (1987) · Zbl 0623.42015
[16] Young, R.M.G., On the best possible constants in the Khintchine inequality, J. London Math. Soc. (2), 14, 3, 496-504, (1976) · Zbl 0364.46012
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.