Geodesic
Two-sided estimates for the constants in Marcinkiewicz's inequalities
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 13, Tome 361 (2008), pp. 45-56

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For symmetric independent random values sharp estimates for the constants in Marcinkiewicz's inequalities are derived. The estimates of the left-hand and right-hand constants are roughly equivalent. Similar estimates for self-normalized sums and new comparative estimates of increasing for some symmetric polynomial are derived, too. Bibl. – 14 titles. 
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     author = {V. A. Egorov},
     title = {Two-sided estimates for the constants in {Marcinkiewicz's} inequalities},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {45--56},
     publisher = {mathdoc},
     volume = {361},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2008_361_a2/}
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V. A. Egorov. Two-sided estimates for the constants in Marcinkiewicz's inequalities. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 13, Tome 361 (2008), pp. 45-56. http://geodesic.mathdoc.fr/item/ZNSL_2008_361_a2/