Geodesic
Estimation of constants for the right-hand inequalities of Marcinkiewicz and Rosenthal
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 11, Tome 341 (2007), pp. 115-123

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Some optimal asymptotic estimates of constants for the right-hand inequalities of Marcinkiewicz and Rosenthal are derived. This estimates imply some new inequalities for the rate of increasing of sums and optimal right-hand estimates for the law of the iterated logarithm. Similar estimates are derived for self-normolized sums. 
@article{ZNSL_2007_341_a5,
     author = {V. A. Egorov},
     title = {Estimation of constants for the right-hand inequalities of {Marcinkiewicz} and {Rosenthal}},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {115--123},
     publisher = {mathdoc},
     volume = {341},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2007_341_a5/}
}
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V. A. Egorov. Estimation of constants for the right-hand inequalities of Marcinkiewicz and Rosenthal. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 11, Tome 341 (2007), pp. 115-123. http://geodesic.mathdoc.fr/item/ZNSL_2007_341_a5/