Rademacher functions in Nakano spaces

Astashkin, Sergey; Mastyło, Mieczysław

doi:10.2140/apde.2016.9.1

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Rademacher functions in Nakano spaces

Sergey Astashkin and Mieczysław Mastyło

Vol. 9 (2016), No. 1, 1–14

DOI: 10.2140/apde.2016.9.1

Abstract

The closed span of Rademacher functions is investigated in Nakano spaces $L^{p (\cdot)}$ on $[0, 1]$ equipped with the Lebesgue measure. The main result of this paper states that under some conditions on distribution of the exponent function $p$ the Rademacher functions form in $L^{p (\cdot)}$ a basic sequence equivalent to the unit vector basis in $ℓ_{2}$ .

Keywords

Rademacher functions, Nakano spaces, symmetric spaces

Mathematical Subject Classification 2010

Primary: 46E30

Secondary: 46B20, 46B42

Milestones

Received: 27 March 2015

Revised: 24 July 2015

Accepted: 7 September 2015

Published: 10 February 2016

Authors

Sergey Astashkin
Department of Mathematics and Mechanics Samara State University Acad. Pavlov, 1 443011 Samara Russia	Samara State Aerospace University (SSAU) Moskovskoye shosse 34 443086, Samara Russia

Mieczysław Mastyło
Faculty of Mathematics and Computer Science Adam Mickiewicz University Collegium Mathematicum Umultowska 87 Street 61-614 Poznań Poland	Institute of Mathematics Polish Academy of Sciences (Poznań branch) ul. Śniadeckich 8 00-656 Warsaw Poland

Vol. 9, No. 1, 2016