Geodesic
A generalization of Campanato--Meyers' theorem
Trudy Instituta matematiki, Tome 20 (2012) no. 2, pp. 30-35

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We prove a generalization of classic Campanato's theorem giving the characterization of Hölder classes on subsets of Euclidean space in terms of the Steklov means behavior. This generalization uses $L^p$-mean oscillation for $p>0,$ and is valid for arbitrary metric space with doubling measure. 
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     title = {A generalization of {Campanato--Meyers'} theorem},
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I. A. Ivanishko; V. G. Krotov; A. I. Porabkovich. A generalization of Campanato--Meyers' theorem. Trudy Instituta matematiki, Tome 20 (2012) no. 2, pp. 30-35. http://geodesic.mathdoc.fr/item/TIMB_2012_20_2_a3/