Estimating Averages of Order Statistics of Bivariate Functions |
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Authors: | Richard Lechner Markus Passenbrunner Joscha Prochno |
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Affiliation: | 1.Institute of Analysis,Johannes Kepler University Linz,Linz,Austria;2.Department of Mathematics,University of Hull,Hull,UK |
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Abstract: | We prove uniform estimates for the expected value of averages of order statistics of bivariate functions in terms of their largest values by a direct analysis. As an application, uniform estimates for the expected value of averages of order statistics of sequences of independent random variables in terms of Orlicz norms are obtained. In the case where the bivariate functions are matrices, we provide a “minimal” probability space which allows us to C-embed certain Orlicz spaces (ell _M^n) into (ell _1^{cn^3}), with (c,C>0) being absolute constants. |
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