Vol. 9, No. 1, 2016

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ISSN: 1948-206X (e-only)
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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 Lp() 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 Lp() a basic sequence equivalent to the unit vector basis in 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