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Bull. Korean Math. Soc. 2013; 50(2): 675-685

Printed March 31, 2013

https://doi.org/10.4134/BKMS.2013.50.2.675

Copyright © The Korean Mathematical Society.

Uniformly bounded composition operators on a Banach space of bounded Wiener-Young variation functions

Dorota G{\l}azowska, Jos\'e Atilio Guerrero, Janusz Matkowski, and Nelson Merentes

University of Zielona G\'{o}ra, Universidad Nacional Experimental del T\'achira, University of Zielona G\'ora, Universidad Central de Venezuela

Abstract

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We prove, under some general assumptions, that a generator of any uniformly bounded Nemytskij operator, mapping a subset of space of functions of bounded variation in the sense of Wiener-Young into another space of this type, must be an affine function with respect to the second variable.

Keywords: $\varphi$-variation in the sense of Wiener, uniformly bounded operator, regularization, composition operator, Jensen equation

MSC numbers: Primary 47B33, 26B30, 26B40; Secondary 39B22

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