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The space of Fourier-Haar multipliers

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Abstract

The Haar system constitutes an unconditional basis for a separable rearrangement invariant (symmetric) space E if and only if the multiplier determined by the sequence \( \lambda _{nk} = \left( { - 1} \right)^n ,k = 0,1, \) for n = 0 and k = 0, 1,..., 2n for n ≥ 1, is bounded in E. If the Lorentz space Λ(ϕ) differs from L1 and L∞ then there is a multiplier with respect to the Haar system which is bounded in Λ(ϕ) and unbounded in L∞ and L1.

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Authors and Affiliations

  1. Tol’yatti State University, Russia

    O. V. Lelond, E. M. Semenov & S. N. Uksusov

  2. Voronezh State University, Russia

    O. V. Lelond, E. M. Semenov & S. N. Uksusov

Authors
  1. O. V. Lelond
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  2. E. M. Semenov
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  3. S. N. Uksusov
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Original Russian Text Copyright © 2005 Lelond O. V., Semenov E. M., and Uksusov S. N.

Translated from Sibirski \( \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{\imath} \) Matematicheski \( \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{\imath} \) Zhurnal, Vol. 46, No. 1, pp. 130–138, January–February, 2005.

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Lelond, O.V., Semenov, E.M. & Uksusov, S.N. The space of Fourier-Haar multipliers. Sib Math J 46, 103–110 (2005). https://doi.org/10.1007/s11202-005-0011-4

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  • DOI: https://doi.org/10.1007/s11202-005-0011-4

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