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SUBSTITUTION OPERATORS IN THE SPACES OF FUNCTIONS OF BOUNDED VARIATION BVα2 (I)
Wadie Aziz,Jos´e Atilio Guerrero,Nelson Merentes 대한수학회 2015 대한수학회보 Vol.52 No.2
The space BVα2 (I) of all the real functions defined on interval I = [a, b] ⊂ R, which are of bounded second α-variation (in the sense De la Vall´e Poussin) on I forms a Banach space. In this space we define an operator of substitution H generated by a function h : I × R → R, and prove, in particular, that if H maps BVα2 (I) into itself and is globally Lipschitz or uniformly continuous, then h is an affine function with respect to the second variable.
Dorota G lazowska,Jos\'e Atilio Guerrero,Janusz Matkowski,Nelson Merentes 대한수학회 2013 대한수학회보 Vol.50 No.2
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.