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Sibirsk. Mat. Zh., 2010, Volume 51, Number 4, Pages 738–750 (Mi smj2121)  

Vector-valued sums of independent functions in rearrangement invariant spaces

S. V. Astashkin

Samara State University, Samara, Russia

Abstract: We obtain some relations that describe the behavior of vector-valued Gaussian sums in rearrangement invariant spaces on the square whose character depends on whether the lower Boyd index of the space is trivial or not. Similar results are proven for the general systems of independent identically and symmetrically distributed random variables.

Keywords: Rademacher functions, Gaussian random variable, independent random variables, rearrangement invariant space, Orlicz space, Boyd indices.

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English version:
Siberian Mathematical Journal, 2010, 51:4, 584–594

Bibliographic databases:

UDC: 517.5+517.982.27
Received: 11.06.2009

Citation: S. V. Astashkin, “Vector-valued sums of independent functions in rearrangement invariant spaces”, Sibirsk. Mat. Zh., 51:4 (2010), 738–750; Siberian Math. J., 51:4 (2010), 584–594

Citation in format AMSBIB
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