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Mat. Zametki, 2004, Volume 76, Issue 4, Pages 483–489 (Mi mz122)  

This article is cited in 14 scientific papers (total in 14 papers)

Comparison of Sums of Independent and Disjoint Functions in Symmetric Spaces

S. V. Astashkina, F. A. Sukochevb

a Samara State University
b Flinders University

Abstract: The sums of independent functions (random variables) in a symmetric space $X$ on $[0,1]$ are studied. We use the operator approach closely connected with the methods developed, primarily, by Braverman. Our main results concern the Orlicz exponential spaces $\exp(L_p)$, $1\leqslant p\leqslant\infty$, and Lorentz spaces $\Lambda_\psi$. As a corollary, we obtain results that supplement the well-known Johnson–Schechtman theorem stating that the condition $L_p\subset X$, $p<\infty$, implies the equivalence of the norms of sums of independent functions and their disjoint “copies”. In addition, a statement converse, in a certain sense, to this theorem is proved.

DOI: https://doi.org/10.4213/mzm122

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English version:
Mathematical Notes, 2004, 76:4, 449–454

Bibliographic databases:

UDC: 517.5+517.982
Received: 12.03.2004

Citation: S. V. Astashkin, F. A. Sukochev, “Comparison of Sums of Independent and Disjoint Functions in Symmetric Spaces”, Mat. Zametki, 76:4 (2004), 483–489; Math. Notes, 76:4 (2004), 449–454

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Astashkin S. V., Sukochev F. A., “Series of independent random variables in rearrangement invariant spaces: An operator approach”, Israel J. Math., 145 (2005), 125–156  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    2. S. V. Astashkin, F. A. Sukochev, “Sums of independent functions in symmetric spaces with the Kruglov property”, Math. Notes, 80:4 (2006), 593–598  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    3. S. V. Astashkin, F. A. Sukochev, “Series of independent mean zero random variables in rearrangement invariant spaces with the Kruglov property”, J. Math. Sci. (N. Y.), 148:6 (2008), 795–809  mathnet  crossref  mathscinet  elib  elib
    4. S. V. Astashkin, “A Generalized Khintchine Inequality in Rearrangement Invariant Spaces”, Funct. Anal. Appl., 42:2 (2008), 144–147  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    5. S. V. Astashkin, “Independent functions in rearrangement invariant spaces and the Kruglov property”, Sb. Math., 199:7 (2008), 945–963  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    6. S. V. Astashkin, “Rademacher functions in symmetric spaces”, Journal of Mathematical Sciences, 169:6 (2010), 725–886  mathnet  crossref  mathscinet  zmath  elib
    7. S. V. Astashkin, D. V. Zanin, E. M. Semenov, F. A. Sukochev, “Kruglov Operator and Operators Defined by Random Permutations”, Funct. Anal. Appl., 43:2 (2009), 83–95  mathnet  crossref  crossref  mathscinet  zmath  isi
    8. S. V. Astashkin, F. A. Sukochev, “Independent functions and the geometry of Banach spaces”, Russian Math. Surveys, 65:6 (2010), 1003–1081  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    9. Astashkin S.V., Sukochev F.A., “BEST CONSTANTS IN ROSENTHAL-TYPE INEQUALITIES AND THE KRUGLOV OPERATOR”, Ann Probab, 38:5 (2010), 1986–2008  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    10. Astashkin S.V., “Rademacher series and isomorphisms of rearrangement invariant spaces on the finite interval and on the semi-axis”, J Funct Anal, 260:1 (2011), 195–207  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    11. S. V. Astashkin, K. E. Tikhomirov, “On Probability Analogs of Rosenthal's Inequality”, Math. Notes, 90:5 (2011), 644–650  mathnet  crossref  crossref  mathscinet  isi
    12. Astashkin S.V., Sukochev F.A., “Symmetric Quasi-Norms of Sums of Independent Random Variables in Symmetric Function Spaces with the Kruglov Property”, Isr. J. Math., 184:1 (2011), 455–476  crossref  mathscinet  zmath  isi  elib  scopus
    13. Astashkin S.V., Tikhomirov K.E., “A Probabilistic Version of Rosenthal's Inequality”, Proc. Amer. Math. Soc., 141:10 (2013), 3539–3547  crossref  mathscinet  zmath  isi  elib  scopus
    14. Junge M., Sukochev F., Zanin D., “Embeddings of Operator Ideals Into l-P-Spaces on Finite Von Neumann Algebras”, Adv. Math., 312 (2017), 473–546  crossref  mathscinet  zmath  isi  scopus  scopus
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