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

Matematicheskie Zametki

RUS ENG

JOURNALS PEOPLE ORGANISATIONS CONFERENCES SEMINARS VIDEO LIBRARY PACKAGE AMSBIB

JavaScript is disabled in your browser. Please switch it on to enable full functionality of the website

	General information
	Latest issue
	Forthcoming papers
	Archive
	Impact factor
	Guidelines for authors
	License agreement
	Submit a manuscript

	Search papers
	Search references

	RSS
	Latest issue
	Current issues
	Archive issues
	What is RSS

Mat. Zametki:
Year:
Volume:
Issue:
Page:
	Find

Personal entry:
Login:
Password:
	Save password
	Enter
	Forgotten password?
	Register

Matematicheskie Zametki, 2004, Volume 76, Issue 4, Pages 483–489
DOI: https://doi.org/10.4213/mzm122 (Mi mzm122)

This article is cited in 16 scientific papers (total in 16 papers)

Comparison of Sums of Independent and Disjoint Functions in Symmetric Spaces

S. V. Astashkin^a, F. A. Sukochev^b

^a Samara State University
^b Flinders University

Full-text PDF (223 kB) Citations (16)

References:

PDF

HTML

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

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.

Received: 12.03.2004

English version:
Mathematical Notes, 2004, Volume 76, Issue 4, Pages 449–454
DOI: https://doi.org/10.1023/B:MATN.0000043474.00734.ec

Bibliographic databases:

UDC: 517.5+517.982

Language: Russian

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

\Bibitem{AstSuk04}

\by S.~V.~Astashkin, F.~A.~Sukochev

\paper Comparison of Sums of Independent and Disjoint Functions in Symmetric Spaces

\jour Mat. Zametki

\yr 2004

\vol 76

\issue 4

\pages 483--489

\mathnet{http://mi.mathnet.ru/mzm122}

\crossref{https://doi.org/10.4213/mzm122}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2112064}

\zmath{https://zbmath.org/?q=an:1076.46020}

\transl

\jour Math. Notes

\yr 2004

\vol 76

\issue 4

\pages 449--454

\crossref{https://doi.org/10.1023/B:MATN.0000043474.00734.ec}

\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000224874900018}

\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-5044227974}

Linking options:

https://www.mathnet.ru/eng/mzm122

https://doi.org/10.4213/mzm122

https://www.mathnet.ru/eng/mzm/v76/i4/p483

This publication is cited in the following 16 articles:

S. V. Astashkin, “Sequences of independent functions and structure of rearrangement invariant spaces”, Russian Math. Surveys, 79:3 (2024), 375–457
Sergey V. Astashkin, The Rademacher System in Function Spaces, 2020, 29
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
Astashkin S.V., Tikhomirov K.E., “A Probabilistic Version of Rosenthal's Inequality”, Proc. Amer. Math. Soc., 141:10 (2013), 3539–3547
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
S. V. Astashkin, K. E. Tikhomirov, “On Probability Analogs of Rosenthal's Inequality”, Math. Notes, 90:5 (2011), 644–650
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
S. V. Astashkin, F. A. Sukochev, “Independent functions and the geometry of Banach spaces”, Russian Math. Surveys, 65:6 (2010), 1003–1081
Astashkin S.V., Sukochev F.A., “BEST CONSTANTS IN ROSENTHAL-TYPE INEQUALITIES AND THE KRUGLOV OPERATOR”, Ann Probab, 38:5 (2010), 1986–2008
S. V. Astashkin, “Rademacher functions in symmetric spaces”, Journal of Mathematical Sciences, 169:6 (2010), 725–886
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
S. V. Astashkin, “A Generalized Khintchine Inequality in Rearrangement Invariant Spaces”, Funct. Anal. Appl., 42:2 (2008), 144–147
S. V. Astashkin, “Independent functions in rearrangement invariant spaces and the Kruglov property”, Sb. Math., 199:7 (2008), 945–963
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
S. V. Astashkin, F. A. Sukochev, “Sums of independent functions in symmetric spaces with the Kruglov property”, Math. Notes, 80:4 (2006), 593–598
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

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Statistics & downloads:
Abstract page:	415
Full-text PDF :	262
References:	57
First page:	1

Registration to the website

Logotypes