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MR2870108 42B25 (46E35)
Lokharu, E. È. Maximal functions that measure smoothness: counterexamples. (Russian) Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 397 (2011), Kraevye Zadachi Matematicheskoĭ Fiziki i Smezhnye Voprosy Teorii Funktsiĭ. 42, 53--72, 172--173; translation in J. Math. Sci. (N.Y.) 185 (2012), no. 5, 687–697
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