The Sobolev space $W_2^{1/2}$: Simultaneous improvement of functions by a homeomorphism of the circle

Vladimir Lebedev

It is known that for every continuous real-valued function $f$ on the circle $\mathbb{T}=\mathbb{R}/2\ddot{I}€\mathbb{Z}$ there exists a change of variable, i.e., a self-homeomorphism $h$ of…