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Optimal constants in the Marcinkiewicz–Zygmund inequalities
Institution:1. Department of Electrical, Electronics, and Telecommunications Engineering and Naval Architecture (DITEN), University of Genoa, Genova, Italy;2. Istituto Italiano di Tecnologia, IIT, Morego, Genova, Italy;1. Laboratoire IMATH, Université de Toulon, BP 20132, 83957 La Garde Cedex, France;2. Dipartimento di Matematica, Università di Pisa, Largo B. Pontecorvo 5, 56127 Pisa, Italy;3. Dipartimento di Matematica e Informatica, Università di Firenze, Viale Morgagni 67/a, 50134 Firenze, Italy;1. Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, 637371, Singapore;2. School of Mathematics and Statistics, Huazhong Normal University, Wuhan 430079, China;3. Beijing Computational Science Research Center, China;4. Wayne State University, Detroit, MI 48202, United States;1. Department of Industrial Engineering, University of Pittsburgh, Pittsburgh, PA 15261, United States;2. Department of Industrial & Systems Engineering, University of Tennessee, Knoxville, TN 37996-2315, United States
Abstract:We give the optimal constants in the Marcinkiewicz–Zygmund inequalities for symmetric summands. As an application we substantially improve the estimates of Ren and Liang (2001) in the Marcinkiewicz–Zygmund–Hölder inequality and identify the best possible constants in the symmetric case.
Keywords:Moment bounds  Khintchine inequalities  Symmetrization
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