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Matematicheskie Zametki, 2016, Volume 100, Issue 4, Pages 483–491
DOI: https://doi.org/10.4213/mzm10634 (Mi mzm10634) 		 
This article is cited in 2 scientific papers (total in 2 papers)

On Fourier Coefficients of Lacunary Systems

S. V. Astashkina, E. M. Semenovb

a Samara State Aerospace University
b Voronezh State University
Full-text PDF (507 kB) Citations (2)
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DOI: https://doi.org/10.4213/mzm10634
Abstract: We prove that the Zygmund space L(lnL)1/2L(lnL)1/2 is the greatest one in the set of symmetric spaces XX for which any uniformly bounded orthonormal system of functions contains a sequence such that the corresponding space of Fourier coefficients F(X)F(X) coincides with ℓ2ℓ2. Similar results also hold for symmetric spaces located between the spaces L(lnL)1/2L(lnL)1/2 and L1L1.
Keywords: orthonormal system, Fourier coefficients, symmetric space, real interpolation method.
Funding agency Grant number
Russian Foundation for Basic Research 14-01-00141а
The work of the first author was supported by the Ministry of Education and Science of the Russian Federation. The work of the second author was supported by the Russian Foundation for Basic Research under grant 14-01-00141a.
Received: 11.11.2014
Revised: 27.03.2016
English version:
Mathematical Notes, 2016, Volume 100, Issue 4, Pages 507–514
DOI: https://doi.org/10.1134/S0001434616090212
Bibliographic databases:
Document Type: Article
UDC: 517.982.22+517.983.23
Language: Russian
Citation: S. V. Astashkin, E. M. Semenov, “On Fourier Coefficients of Lacunary Systems”, Mat. Zametki, 100:4 (2016), 483–491; Math. Notes, 100:4 (2016), 507–514
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/mzm/v100/i4/p483
    • This publication is cited in the following 2 articles:
    1. M. Junge, F. Sukochev, D. Zanin, “Embeddings of operator ideals intoLp-spaces on finite von Neumann algebras”, Advances in Mathematics, 312 (2017), 473  crossref
    2. Sergey V. Astashkin, “Rademacher series and isomorphisms of rearrangement invariant spaces on the finite interval and on the semi-axis”, Journal of Functional Analysis, 260:1 (2011), 195  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математические заметки Mathematical Notes
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