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UNIFORMLY BOUNDED COMPOSITION OPERATORS ON A BANACH SPACE OF BOUNDED WIENER-YOUNG VARIATION FUNCTIONS

Glazowska, Dorota;Guerrero, Jose Atilio;Matkowski, Janusz;Merentes, Nelson

  • Received : 2012.01.17
  • Published : 2013.03.31

Abstract

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

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