Le calcul fonctionnel sous-linéaire dans les espaces de Besov homogènes

Revista Matematica Iberoamericana

Volumn 22, Issue 2, 2006, Pages 725-746

  Bourdaud, Gérard ^a   Meyer, Yves ^b  

^a INSTITUT DE MATHÉMATIQUES DE JUSSIEU   (France)

^b Inserm   (France)

Author keywords

Bounded variation; Composition operators; Homogeneous besov spaces

Indexed keywords

EID: 33846688664     PISSN: 02132230     EISSN: 22350616     Source Type: Journal    
DOI: 10.4171/RMI/472     Document Type: Review

References (27)

1. BESOV, O. V.: Investigation of a class of function spaces in connection with imbedding and extension theorems. (Russian) Trudy. Mat. Inst. Steklov 60 (1961), 42-81.
2. BONY, J. M.: Calcul symbolique et propagation des singularités pour les équations aux dérivées partielles non linéaires. Ann. Sci. École Norm. Sup. (4) 14 (1981), 209-246.
3. BOURDAUD, G.: Réalisations des espaces de Besov homogènes. Ark. Mat. 26 (1988), 41-54.
4. BOURDAUD, G.: Fonctions qui opèrent sur les espaces de Besov et de Triebel. Ann. Inst. H. Poincaré Anal. Non Linéaire 10 (1993), 413-422.
5. BOURDAUD, G.: Ce qu'il faut savoir sur les espaces de Besov. Prépub. Univ. Paris 7 - URA 212, 53 (1993).
6. BOURDAUD, G.: The functional calculus in Sobolev spaces. In Function spaces, differential operators and non linear analysis (Friedrichroda, 1992), 127-142. Teubner-Texte Math. 133. Teubner, Stuttgart, 1993.
7. BOURDAUD, G.: Calcul fonctionnel dans certains espaces de Lizorkin-Triebel. Arch. Math. (Basel) 64 (1995), 42-47.
8. BOURDAUD, G.: Ondelettes et espaces de Besov. Rev. Mat. Iberoamericana 11 (1995), no. 3, 477-512.
9. BOURDAUD, G.: Superposition operators in Zygmund and BMO spaces. In Function spaces, differential operators and non linear analysis (Teistungen, 2001), 59-74. Birkhäuser, Basel, 2003.
10. BOURDAUD, G. AND KATEB, M. E. D.: Calcul fonctionnel dans l'espace de Sobolev fractionnaire. Math. Z. 210 (1992), 607-613.
11. BOURDAUD, G. AND KATEB, M. E. D. : Fonctions qui opèrent sur les espaces de Besov. Math. Ann. 303 (1995), 653-675.
12. BOURDAUD, G. AND LANZA DE CRISTOFORIS, M.: Functional calculus in Hölder-Zygmund spaces. Trans. Amer. Math. Soc. 354 (2002), 4109-4129.
13. BOURDAUD, G., LANZA DE CRISTOFORIS, M. AND SICKEL, W.: Superposition operators and functions of bounded p-variation. Rev. Mat. Iberoamericana, 22 (2006), no. 2.
14. BOURDAUD, G. AND MEYER, Y.: Fonctions qui opèrent sur les espaces de Sobolev. J. Funct Anal. 97 (1991), 351-360.
15. CHEMIN, J.-Y.: Fluides parfaits incompressibles. Astérisque 230 (1995).
16. DEVORE, R. A. AND LORENTZ, G. G.: Constructive approximation. Fundamental Principles of Mathematical Sciences 303. Springer, Berlin, 1993.
17. s of Triebel-Lizorkin type: pointwise multipliers and spaces on domains. Math. Nachr. 125 (1986), 29-68.
18. LEMARIÉ-RIEUSSET, P. G.: Recent developments in the Navier-Stokes problem. Chapman Hall/CRC Research Notes in Mathematics 431. Chapman Hall/CRC, Boca Raton, FL, 2002.
19. MEYER, Y.: Oscillating patterns in image processing and nonlinear evolution equations. The fifteenth Dean Jacqueline B. Lewis memorial lectures. University Lecture Series, 22, Amer. Math. Soc., Providence, RI, 2001.
20. OSWALD, P.: On the boundedness of the mapping f → |f| in Besov spaces. Comment. Math. Univ. Carolin. 33 (1992), 57-66.
21. PEETRE, J.: Interpolation of Lipschitz operators and metric spaces. Mathematica (Cluj) 12 (1970), 325-334.
22. PEETRE, J.: New thoughts on Besov spaces. Duke Univ. Math. Series I. Mathematics Department, Duke University, Durham, N.C., 1976.
23. RUNST, T. AND SICKEL, W.: Sobolev spaces of fractional order, Nemytskij operators, and nonlinear partial differential equations. De Gruyter Series in Nonlinear Analysis and Applications 3. Walter de Gruyter, Berlin, 1996.
24. SAVARÉ, G.: On the regularity of the positive part of functions. Nonlinear Anal. 27 (1996), no. 9, 1055-1074.
25. SAVARÉ, G. AND TOMARELLI, F.: Superposition and chain rule for bounded Hessian functions. Adv. Math. 140 (1998), 237-281.
26. TRIEBEL, H.: Interpolation theory, function spaces, differential operators. North-Holland Mathematical Library 18. North-Holland, Amsterdam-New York, 1978.
27. TRIEBEL, H. : Theory of function spaces II. Monographs in Mathematics 84. Birkhäuser, Basel, 1992.