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 ℓ 2. 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 L 1.
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Original Russian Text © S. V. Astashkin, E. M. Semenov, 2016, published in Matematicheskie Zametki, 2016, Vol. 100, No. 4, pp. 483–491.
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Astashkin, S.V., Semenov, E.M. On Fourier coefficients of lacunary systems. Math Notes 100, 507–514 (2016). https://doi.org/10.1134/S0001434616090212
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DOI: https://doi.org/10.1134/S0001434616090212