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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
Abstract:
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, Fourier coefficients, symmetric space, real interpolation method.
Received: 11.11.2014 Revised: 27.03.2016
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
Linking options:
https://www.mathnet.ru/eng/mzm10634https://doi.org/10.4213/mzm10634 https://www.mathnet.ru/eng/mzm/v100/i4/p483
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Abstract page: | 428 | Full-text PDF : | 68 | References: | 74 | First page: | 36 |
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