This article is cited in 1 paper

Paley spaces

S. V. Astashkin^a, E. M. Semenov<sup>b

a</sup> Samara State University, Samara, Russia
^b Voronezh State University, Voronezh, Russia

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.

UDC: 517.982.22+517.983.23

Received: 25.12.2013

 English version: Siberian Mathematical Journal, 2015, 56:1, 21–27

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