Revistes Catalanes amb Accés Obert (RACO)

On the composition operator in $\mathcal{AC}[a,b]$

Nelson Merentes

Resum


Denote by $F$ the composition operator generated by a given function $f:\mathbb{R}\rightarrow\mathbb{R}$, acting on the space of absolutely continuous functions. In this paper we prove that the composition operator $F$ maps the space $\mathcal{AC}[a,b]$ into itself if and only if $f$ satisfies a local Lipschitz condition on $\mathbb{R}$

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