Abstract
Let x be an integrable function on [0, 1] and let Px be the Paley function constructed from the expansion of x in the Fourier-Haar series. If E is a rearrangement invariant space on [0, 1] then P(E) stands for the space with the norm ‖Px‖ E . Among other results, we prove that P(E) is reflexive if and only if so is E.
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Original Russian Text Copyright © 2015 Astashkin S.V. and Semenov E.M.
The authors were supported by the Russian foundation for Basic Research (Grants 12-01-00198a and 11-01-00614a).
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Samara and Voronezh. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 56, No. 1, pp. 27–35, January–February, 2015.
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Astashkin, S.V., Semenov, E.M. Paley spaces. Sib Math J 56, 21–27 (2015). https://doi.org/10.1134/S0037446615010036
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DOI: https://doi.org/10.1134/S0037446615010036