Geodesic
About the boundedness of the Fourier–Haar multiplicators
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 2 (2010), pp. 24-31 Cet article a éte moissonné depuis la source Math-Net.Ru

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The boundedness of the Fourier–Haar multiplicators defined by the sequence $\lambda_{k,i}=\varepsilon_k=\pm 1,\;i=m$ and $\lambda_{k,i}=1$, if $i\neq m$, $m\in \mathbb N$, $m\geqslant 2$ is considered. The equivalent conditions to the unconditional basis of the Haar system are received.
Keywords: Haar system, rearrangement invariant space, multiplicators, absolute basis, series of the Fourier–Haar. 
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R. Zh. Gamil'yanov; R. F. Uzbekov. About the boundedness of the Fourier–Haar multiplicators. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 2 (2010), pp. 24-31. http://geodesic.mathdoc.fr/item/VSGU_2010_2_a2/

[1] Krein S. G., Petunin Yu. I., Semenov E. M., Interpolyatsiya lineinykh operatorov, Nauka, M., 1978 | MR

[2] Kashin B. S., Saakyan A. L., Ortogonalnye ryady, AFTs, M., 1999 | MR | Zbl

[3] Novikov I., Semenov E., Haar series and linear operators, Kluwer Acad. Publ., Dordrecht, 1997 | MR

[4] Bryskin I. B., Lelond O. V., Semenov E. M., “Multiplikatory ryadov Fure–Khaara”, Sib. mat. zhurnal, 41:4 (2000), 758–766 | MR | Zbl

[5] Uksusov S. N., Multiplikatory Fure–Khaara v simmetrichnykh prostranstvakh, dis. $\dots$ kand. fiz.-mat. nauk, Voronezh, 2006