Geodesic
A correction theorem for functions with integral smoothness
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 26, Tome 255 (1998), pp. 17-35

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A theorem similar to the correction theorem of K. Oskolkov is proved. Namely, for a function with a given $k$th modulus of continuity calculated in a symmetric space $X$, for every $\epsilon>0$ a set is presented whose measure is at least $1-\epsilon$ and on which a sharp quantitative estimate of the uniform $k$th modulus of continuity of this function is given. It is shown that this estimate depends only on $\epsilon$ and on the fundamental function of the symmetric space. 
@article{ZNSL_1998_255_a1,
     author = {E. I. Berezhnoi},
     title = {A correction theorem for functions with integral smoothness},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {17--35},
     publisher = {mathdoc},
     volume = {255},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1998_255_a1/}
}
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E. I. Berezhnoi. A correction theorem for functions with integral smoothness. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 26, Tome 255 (1998), pp. 17-35. http://geodesic.mathdoc.fr/item/ZNSL_1998_255_a1/