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JOURNALS // Trudy Matematicheskogo Instituta imeni V.A. Steklova // Archive
Trudy Mat. Inst. Steklova, 2003 Volume 243, Pages 53–65 (Mi tm420)
This article is cited in 14 papers

Characterizations of the Nikol'skii–Besov and Lizorkin–Triebel Function Spaces of Mixed Smoothness

D. B. Bazarkhanov

Institute of Mathematics and Mechanics, Kazakhstan National Academy of Sciences

Abstract: The Nikol'skii–Besov and Lizorkin–Triebel function spaces of mixed positive smoothness are characterized in terms of fairly general (including local) averages and Peetre maximal functions. Atomic decompositions for functions from these spaces are also obtained.

UDC: 517.5

Received in March 2003


 English version: Proceedings of the Steklov Institute of Mathematics, 2003, 243, 46–58

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