Functional calculus in Hölder-Zygmund spaces

Transactions of the American Mathematical Society

Volumn 354, Issue 10, 2002, Pages 4109-4129

  Bourdaud, G ^a   Lanza de Cristoforis, Massimo ^a  

^a INSTITUT DE MATHÉMATIQUES DE JUSSIEU   (France)

Author keywords

Composition operators; H lder Zygmund spaces

Indexed keywords

EID: 0036786060     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0002-9947-02-03000-3     Document Type: Article

References (21)

1. J. Appell and P.P. Zabreiko, Nonlinear Superposition Operators, Cambridge Tracts in Mathematics 95, Cambridge University Press, Cambridge (1990). MR 91k:47168
2. C. Bennett and R. Sharpley, Interpolation of Operators, Pure and Applied Mathematics 129, Academic Press, Boston (1988). MR 89e:46001
3. G. Bourdaud, Le calcul fonctionnel dans les espaces de Sobolev, Invent. Math., 104 (1991), pp. 435-446. MR 93b:46053
4. G. Bourdaud, Fonctions qui opèrent sur les espaces de Besov et de Triebel, Ann. Inst. Henri Poincaré, Analyse non linéaire, 10 (1993), pp. 413-422. MR 94m:46055
5. G. Bourdaud, Analyse fonctionnelle dans l'espace Euclidien, 2ième édition, Pub. Math. Univ. Paris 7 (1995). MR 89a:46001 (1st ed.)
6. P. Drábek, Continuity of Nemyckij's operator in Hölder spaces, Comm. Math. Univ. Carolinae, 16 (1975), pp. 37-57. MR 52:1447
7. G.B. Folland, Real analysis, modern techniques and their applications, John Wiley and Sons, New York (1984). MR 86k:28001
8. Y. Katznelson, An introduction to Harmonic Analysis, Dover, New York (1976). MR 54:10976
9. H. Koch and W. Sickel, Pointwise multipliers of Besov spaces of smoothness zero and spaces of continuous functions, Rev. Math. Iberoamericana (to appear).
10. A. Kufner, O. John and S. Fučik, Function Spaces, Noordhoff International Publishing, Leyden (1977). MR 58:2189
11. M. Lanza de Cristoforis, Higher order differentiability properties of the composition and of the inversion operator, Indag. Matem. N.S., 5 (1994), pp. 457-482. MR 95j:47081
12. M. Lanza de Cristoforis, Differentiability properties of an abstract autonomous composition operator, J. London Math. Soc. 61 (2000), pp. 923-936. MR 2001c:47069
13. A. Marchaud, Sur les dérivées et sur les différences des fonctions des variables réelles, J. Math. Pure et Appl. 6 (1927), pp. 337-425.
14. J. Peetre, New Thoughts on Besov spaces, Duke University Mathematics Series, No. 1. Mathematics Department, Duke University, Durham, N.C. (1976). MR 57:1108
15. T. Runst and W. Sickel, Sobolev Spaces of Fractional Order, Nemytskij Operators, and Nonlinear Partial Differential Equations, De Gruyter, Berlin (1996). MR 98a:47071
16. E. P. Sobolevskij, The superposition operator in Hölder spaces, Voronezh, VINITI No. 3765-84 (1984), (in Russian).
17. P.M. Tamrazov, Structural and approximational properties of functions in the complex domain, Linear Spaces and Approximation, Birkhäuser, Basel, (1978), pp. 503-514. MR 80a:30044
18. P.M. Tamrazov, Divided differences and moduli of smoothness of functions, function superpositions and their application, Constructive theory of functions 1984, Sofia, 1984, pp. 840-851.
19. H. Triebel, Theory of Function Spaces II, Birkhäuser, Basel (1992). MR 93f:46029
20. S.E. Warschawski, On the higher derivatives at the boundary in conformal mapping, Trans. Amer. Math. Soc. 38 (1935), pp. 310-340
21. A. Zygmund, Trigonometric Series, Cambridge University Press, New York (1959). MR 21:6498