Geodesic
Reconstruction of functions with the given modulus of continuity
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part IX, Tome 92 (1979), pp. 203-219 
A. A. Moisejev. Reconstruction of functions with the given modulus of continuity. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part IX, Tome 92 (1979), pp. 203-219. http://geodesic.mathdoc.fr/item/ZNSL_1979_92_a11/
@article{ZNSL_1979_92_a11,
     author = {A. A. Moisejev},
     title = {Reconstruction of functions with the given modulus of continuity},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {203--219},
     year = {1979},
     volume = {92},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1979_92_a11/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

Let $\mu$ be a measure on $[a,b],C_{\omega,\mu}$ the class of all functions $f$ whose continuity modulus does not exceed the given function $\omega$ and such that $\int_a^bf\,d\mu=0$. The problem of eatimatinq $\operatorname{diam}C_{\omega,\mu}$ (in the space $C([a,b])$) is reduced to an equilibrium problem for the “potential” $\int\omega(|x-t|)\,d\mu(t)$.