Uniformly bounded superposition operators in the space of functions of bounded n-dimensional Φ-variation

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Uniformly bounded superposition operators in the space of functions of bounded n-dimensional Φ-variation

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Title: Uniformly bounded superposition operators in the space of functions of bounded n-dimensional Φ-variation
Author: Bracamonte, M.; Ereú, J.; Giménez, J.; Merentes, N.
Abstract: We prove that if a superposition operator maps a subset of the space of all functions of n-dimensional bounded Φ-variation in the sense of Riesz, into another such space, and is uniformly bounded, then the non-linear generator h(x, y) of this operator must be of the form h(x, y) = A(x)y + B(x) where, for every x, A(x) is a linear map.
URI: http://hdl.handle.net/10662/10071
Date: 2014


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