Lemarié, Pierre-Gilles Continuité sur les espaces de Besov des opérateurs définis par des intégrales singulières. (French) Zbl 0555.47032 Ann. Inst. Fourier 35, No. 4, 175-187 (1985). 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. Cited in 1 ReviewCited in 16 Documents MSC: 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) Keywords:singular integral operators; homogeneous Besov spaces; paraproduct operator PDF BibTeX XML Cite \textit{P.-G. Lemarié}, Ann. Inst. Fourier 35, No. 4, 175--187 (1985; Zbl 0555.47032) Full Text: DOI Numdam EuDML References: [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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.