In this paper we prove sufficent conditions on a map f from the real line to itself in order that the composite map f ◦ g belongs to a Sobolev Morrey space of real valued functions on a domain of the n-dimensional space for all functions g in such a space. Then we prove sufficient conditions on f in order that the composition operator T_f defined by T_f[g]≡f◦g for all functions g in the Sobolev Morrey space is continuous, Lipschitz continuous and differentiable in the Sobolev Morrey space. We confine the attention to Sobolev Morrey spaces of order up to one.

The composition operator in Sobolev Morrey spaces

KYDYRMINA, NURGUL;LANZA DE CRISTOFORIS, MASSIMO
2016

Abstract

In this paper we prove sufficent conditions on a map f from the real line to itself in order that the composite map f ◦ g belongs to a Sobolev Morrey space of real valued functions on a domain of the n-dimensional space for all functions g in such a space. Then we prove sufficient conditions on f in order that the composition operator T_f defined by T_f[g]≡f◦g for all functions g in the Sobolev Morrey space is continuous, Lipschitz continuous and differentiable in the Sobolev Morrey space. We confine the attention to Sobolev Morrey spaces of order up to one.
2016
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11577/3216698
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