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.
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Original Russian Text Copyright © 2010 Astashkin S. V.
The author expresses his gratitude to the reviewer whose suggestions and remarks allowed him to improve the text of the article, in particular, to simplify the proof of Lemma 4.
Samara. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 51, No. 4, pp. 738–750, July–August, 2010.
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Astashkin, S.V. Vector-valued sums of independent functions in rearrangement invariant spaces. Sib Math J 51, 584–594 (2010). https://doi.org/10.1007/s11202-010-0060-1
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DOI: https://doi.org/10.1007/s11202-010-0060-1