Lipschitzian Superposition Operators Between Spaces of Functions of Bounded Generalized Variation with Weight
Copyright policy )Lipschitzian Superposition Operators Between Spaces of Functions of Bounded Generalized Variation with Weight
The author presents several properties of function spaces of bounded generalized variation of Riesz-Orlicz type including weight and then proves that each globally Lipschitzian superposition (or Nemytskij) operators between two such spaces must be affine. The first result of this type for the spaces of Lipschitzian functions has been proved by the reviewer [Funkc. Ekvacioj, Ser. Int. 25, 127-132 (1982; Zbl 0504.39008)]. For some other function spaces this problem was also considered by several authors. The first result for multivalued operators is due to \textit{A. Smajdor} and \textit{W. Smajdor} [Rad. Mat. 5, No. 2, 311-320 (1989; Zbl 0696.47057)].
- National Research University Higher School of Economics Russian Federation
Banach algebras of continuous functions, function algebras, Linear operators on function spaces (general), Functions of bounded variation, generalizations, Lipschitzian superposition operator, bounded generalized variation of Riesz-Orlicz type, weight, Particular nonlinear operators (superposition, Hammerstein, Nemytskiĭ, Uryson, etc.)
Banach algebras of continuous functions, function algebras, Linear operators on function spaces (general), Functions of bounded variation, generalizations, Lipschitzian superposition operator, bounded generalized variation of Riesz-Orlicz type, weight, Particular nonlinear operators (superposition, Hammerstein, Nemytskiĭ, Uryson, etc.)
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