2025/11/11 by Lebedev, Vladimir
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Primary 42A16
paper · doi:10.48550/arxiv.2511.07840
It is known that for every continuous real-valued function f on the circle \mathbb T=\mathbb R/2π\mathbb Z there exists a change of variable, i.e., a self-homeomorphism h of \mathbb T, such that the superposition f∘ h is in the Sobolev space W21/2(\mathbb T). We obtain new results on simultaneous improvement of functions by a single change of variable in relation to the space W21/2(\mathbb T). The main result is as follows: there does not exist a self-homeomorphism h of \mathbb T such that f∘ h∈ W21/2(\mathbb T) for every f∈ Lip1/2(\mathbb T). Here Lip1/2(\mathbb T) is the class of all functions on \mathbb T satisfying the Lipschitz condition of order 1/2.