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Continuité sur les espaces de Besov des opérateurs définis par des intégrales singulières. (French) Zbl 0555.47032
The author gives a very simple criterion for singular integral operators to be bounded on homogeneous Besov spaces \(\dot B^ s_{p,q}\) for \(0<s<1\). The use of this criterion is then illustrated by some examples, mainly by using the paraproduct operator.

47Gxx Integral, integro-differential, and pseudodifferential operators
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
45P05 Integral operators
47B38 Linear operators on function spaces (general)
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[1] A. P. CALDERÓN and A. ZYGMUND, Singular integral operators and differential equations, Amer. J. Math., 9 (1957), 801-821. · Zbl 0081.33502
[2] R. R. COIFMAN et Y. MEYER, Au-delà des opérateurs pseudo-différentiels, Astérisque, 57 (1978). · Zbl 0483.35082
[3] G. DAVID et J.-L. JOURNÉ, Une caractérisation des opérateurs intégraux singuliers bornés sur L²(rn), C.R.A.S., Paris, 296 (16 Mai 1983), 761-764. · Zbl 0523.45009
[4] G. B. FOLLAND, Lipschitz classes and Poisson integrals on stratified groups, Studia Math., 66 (1979), 37-55. · Zbl 0439.43005
[5] P. G. LEMARIE, Algèbres d’opérateurs et semi-groupes de Poisson sur un espace de nature homogène, Publications Mathématiques d’Orsay, 1984. · Zbl 0598.58045
[6] M. MEYER, Thèse de 3e cycle, Orsay.
[7] Y. MEYER, LES nouveaux opérateurs de Calderón-Zygmund. actes du colloque L. Schwartz, École Polytechnique, Juin 1983 (à paraître dans Astérisque, SMF). · Zbl 0573.42010
[8] K. SAKA, Besov spaces and Sobolev spaces on a nilpotent Lie group, Tohoku Math. J., 31 (1979), 383-437. · Zbl 0429.43004
[9] E. M. STEIN, Singular integral operators and differentiability properties of functions, Princeton Univ. Press, Princeton, N. J., 1970. · Zbl 0207.13501
[10] H. TRIEBEL, Theory of function spaces, Birkhäuser Verlag, Basel-Boston-Stuttgart, 1983. · Zbl 0546.46027
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