Geodesic
On the integrability of a maximal square function in ergodic theory
Teoriâ veroâtnostej i ee primeneniâ, Tome 44 (1999) no. 2, pp. 432-440 Cet article a éte moissonné depuis la source Math-Net.Ru

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Necessary and sufficient conditions are established for $L^2$-summability of the maximal square function of general unitary operators. Extensions of the result to arbitrary contractions in $L^2$, multiparameter unitary groups, and power-bounded operators in $L^p$, $p>1$, are considered as well.
Keywords: unitary operators, contractive operators, homogeneous random fields, power-bounded operators, individual ergodic theorem, maximal square function. 
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     author = {V. F. Gaposhkin},
     title = {On the integrability of a maximal square function in ergodic theory},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {432--440},
     year = {1999},
     volume = {44},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1999_44_2_a10/}
}
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V. F. Gaposhkin. On the integrability of a maximal square function in ergodic theory. Teoriâ veroâtnostej i ee primeneniâ, Tome 44 (1999) no. 2, pp. 432-440. http://geodesic.mathdoc.fr/item/TVP_1999_44_2_a10/