This article is cited in 10 papers

Equivalent (Quasi)Norms for Certain Function Spaces of Generalized Mixed Smoothness

D. B. Bazarkhanov

Institute of Mathematics and Mechanics, Kazakhstan National Academy of Sciences

Abstract: For certain (quasi)Banach function spaces of generalized mixed positive smoothness defined by (mixed) weighted norms of smooth dyadic decompositions of their Fourier transforms, characterizations are obtained in terms of rather general averages, their Peetre maximal functions, atomic and molecular representations, as well as in terms of the so-called $\varphi$-transforms.

UDC: 517.518

Received in October 2004

 English version: Proceedings of the Steklov Institute of Mathematics, 2005, 248, 21–34

Bibliographic databases:

• 
•