Geodesic
Equivalent Normings of Spaces of Functions of Variable Smoothness
Informatics and Automation, Function spaces, approximations, and differential equations, Tome 243 (2003), pp. 87-95.

Voir la notice de l'article provenant de la source Math-Net.Ru

For the Banach spaces $B_{p,q}^a$ and $F_{p,q}^a$ of functions defined on $\mathbb R^n$ whose variable smoothness $a=a(x)$ is determined by the behavior of their differences, equivalent normings are established in terms of weighted norms of smooth dyadic decompositions of their Fourier transforms. 
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O. V. Besov. Equivalent Normings of Spaces of Functions of Variable Smoothness. Informatics and Automation, Function spaces, approximations, and differential equations, Tome 243 (2003), pp. 87-95. http://geodesic.mathdoc.fr/item/TRSPY_2003_243_a7/

[1] Besov O. V., Ilin V. P., Nikolskii S. M., Integralnye predstavleniya funktsii i teoremy vlozheniya, Nauka, M., 1996 | MR

[2] Triebel H., Theory of function spaces, Birkhäuser, Basel, 1983 ; Tribel Kh., Teoriya funktsionalnykh prostranstv, Mir, M., 1986 | MR | Zbl | MR | Zbl

[3] Besov O. V., “Vlozheniya prostranstv differentsiruemykh funktsii peremennoi gladkosti”, Tr. MIAN, 214, 1997, 25–58 | MR | Zbl

[4] Besov O. V., “O prostranstvakh funktsii peremennoi gladkosti, opredelyaemykh psevdodifferentsialnymi operatorami”, Tr. MIAN, 227, 1999, 56–74 | MR | Zbl

[5] Kalyabin G. A., Lizorkin P. I., “Spaces of functions of generalized smoothness”, Math. Nachr., 133 (1987), 7–32 | DOI | MR | Zbl

[6] Merucci C., “Applications of interpolation with a function parameter to Lorenz, Sobolev and Besov spaces”, Lect. Notes Math., 1070, 1984, 183–201 | MR | Zbl

[7] Cobos P., Fernandez D. L., “Hardy–Sobolev spaces and Besov spaces with a function parameter”, Lect. Notes Math., 1302, 1988, 158–170 | MR | Zbl

[8] Leopold H.-G., Pseudodifferentialoperatoren und Funktionenräume variabler Glattheit, Diss. B., Friedrich-Schiller-Univ., Jena, 1987

[9] Leopold H.-G., “On function spaces of variable order of differentiation”, Forum Math., 3:1 (1991), 1–21 | DOI | MR | Zbl

[10] Triebel H., “Maximal inequalities, Fourier multipliers, Littlewood–Paley theorems, and approximations by entire analytic functions in weighted spaces”, Anal. Math., 6:1 (1980), 87–103 | DOI | MR | Zbl

[11] Björck G., “Linear partial differential operators and generalized distributions”, Ark. Mat., 6 (1966), 351–407 | DOI | MR | Zbl

[12] Beurling A., Quasi-analyticity and general distributions, Lect. 4, 5, AMS Summer Inst., Stanford, 1961