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Sovolevskij, E.P. (1984) The Superposition Operator in Hölder Spaces. (Russian). VINITI No. 3765-84, Voronezh.

has been cited by the following article:

• TITLE: Locally Defined Operators and Locally Lipschitz Composition Operators in the Space WBVp(·)([a, b])

  AUTHORS: José Atilio Guerrero, Odalis Mejía, Nelson Merentes

  KEYWORDS: Generalized Variation, p(·)-Variation in Wiener’s Sense, Variable Exponent, Convergence, Helly’s Theorem, Local Operator

  JOURNAL NAME: Advances in Pure Mathematics, Vol.6 No.10, September 27, 2016

  ABSTRACT: We give a neccesary and sufficient condition on a functionsuch that the composition operator (Nemytskij Operator) H defined by acts in the space and satisfies a local Lipschitz condition. And, we prove that every locally defined operator mapping the space of continuous and bounded Wiener p(·)-variation with variable exponent functions into itself is a Nemytskij com-position operator.