No self-homeomorphism h of the circle exists such that f ∘ h lies in W_2^{1/2}(T) for every f in Lip_{1/2}(T).
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The Sobolev space $W_2^{1/2}$: Simultaneous improvement of functions by a homeomorphism of the circle
No self-homeomorphism h of the circle exists such that f ∘ h lies in W_2^{1/2}(T) for every f in Lip_{1/2}(T).