Geodesic
Estimates for a~uniform modulus of continuity of functions from symmetric spaces
Izvestiya. Mathematics , Tome 60 (1996) no. 2, pp. 233-250.

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We prove a multidimensional “correctability” theorem of the Oskolkov type for a function given in $\mathbb R^n$ whereby a sharp quantitative estimate for the uniform modulus of continuity of a function on “large” sets is given if an estimate of the modulus of continuity of this function in a symmetric space is known. We show that an estimate of a uniform modulus of continuity depends only on the eigenfunction of the symmetric space. 
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E. I. Berezhnoi. Estimates for a~uniform modulus of continuity of functions from symmetric spaces. Izvestiya. Mathematics , Tome 60 (1996) no. 2, pp. 233-250. http://geodesic.mathdoc.fr/item/IM2_1996_60_2_a0/

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