Email this article On Fourier coefficients of lacunary systems
- Authors: Astashkin S.V.1, Semenov E.M.2
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Affiliations:
- Korolev Samara National Research University
- Voronezh State University
- Issue: Vol 100, No 3-4 (2016)
- Pages: 507-514
- Section: Article
- URL: https://journals.rcsi.science/0001-4346/article/view/149752
- DOI: https://doi.org/10.1134/S0001434616090212
- ID: 149752
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Abstract
We prove that the Zygmund space L(lnL)1/2 is the largest among symmetric spaces X in which any uniformly bounded orthonormal system of functions contains a sequence such that the corresponding space of Fourier coefficients F(X) coincides with ℓ2. Moreover, we obtain a description of spaces of Fourier coefficients corresponding to appropriate subsequences of arbitrary uniformly bounded orthonormal systems in symmetric spaces located between the spaces L(lnL)1/2 and L1.
About the authors
S. V. Astashkin
Korolev Samara National Research University
Author for correspondence.
Email: astash@samsu.ru
Russian Federation, Samara
E. M. Semenov
Voronezh State University
Email: astash@samsu.ru
Russian Federation, Voronezh
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