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Superposition operators in Sobolev spaces. (English. Russian original) Zbl 1033.47020

Russ. Math. 46, No. 10, 9-31 (2002); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2002, No. 10, 11-33 (2002).
A characterization of the superposition operators \(\varphi^*(f)=f\circ \varphi\) in terms of the generating function \(\varphi\) is given for certain Sobolev spaces. The obtained facts extend the ones discussed in a previous paper by the authors [Sib. Mat. Zh. 39, 776–795 (1998; Zbl 0917.46023)].

MSC:

47B33 Linear composition operators
30C65 Quasiconformal mappings in \(\mathbb{R}^n\), other generalizations
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems

Citations:

Zbl 0917.46023
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