Geodesic
On Fourier Coefficients of Lacunary Systems
Matematičeskie zametki, Tome 100 (2016) no. 4, pp. 483-491

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We prove that the Zygmund space $L(\ln L)^{1/2}$ is the greatest one in the set of symmetric spaces $X$ for which any uniformly bounded orthonormal system of functions contains a sequence such that the corresponding space of Fourier coefficients $F(X)$ coincides with $\ell_2$. Similar results also hold for symmetric spaces located between the spaces $L(\ln L)^{1/2}$ and $L_1$.
Keywords: orthonormal system, symmetric space, real interpolation method.
Mots-clés : Fourier coefficients 
@article{MZM_2016_100_4_a0,
     author = {S. V. Astashkin and E. M. Semenov},
     title = {On {Fourier} {Coefficients} of {Lacunary} {Systems}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {483--491},
     publisher = {mathdoc},
     volume = {100},
     number = {4},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2016_100_4_a0/}
}
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S. V. Astashkin; E. M. Semenov. On Fourier Coefficients of Lacunary Systems. Matematičeskie zametki, Tome 100 (2016) no. 4, pp. 483-491. http://geodesic.mathdoc.fr/item/MZM_2016_100_4_a0/