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Sibirskii Matematicheskii Zhurnal, 2015, Volume 56, Number 1, Pages 27–35 (Mi smj2619)  
This article is cited in 1 scientific paper (total in 1 paper)

Paley spaces

S. V. Astashkina, E. M. Semenovb

a Samara State University, Samara, Russia
b Voronezh State University, Voronezh, Russia
Full-text PDF (317 kB) Citations (1)
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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 $E$.
Keywords: rearrangement invariant space, Haar function, Paley function, real interpolation method.
Received: 25.12.2013
English version:
Siberian Mathematical Journal, 2015, Volume 56, Issue 1, Pages 21–27
DOI: https://doi.org/10.1134/S0037446615010036
Bibliographic databases:
Document Type: Article
UDC: 517.982.22+517.983.23
Language: Russian
Citation: S. V. Astashkin, E. M. Semenov, “Paley spaces”, Sibirsk. Mat. Zh., 56:1 (2015), 27–35; Siberian Math. J., 56:1 (2015), 21–27
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Сибирский математический журнал Siberian Mathematical Journal
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