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Superposition of functions in Sobolev spaces of fractional order. A survey
(0.2) TG(H s0 p (R )) → H1 p (R ) , s1 ≤ s0 . Since the paper of Dahlberg [7] it is known that one cannot expect s0 = s1 in general. The loss of smoothness under the superposition, even in the case G ∈ C(R), depends on …