L2 Estimates for Weyl Quantization

Journal of Functional Analysis

Volumn 165, Issue 1, 1999, Pages 173-204

  Boulkhemair, A ^a  

^a UNIVERSITÉ DE NANTES   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001421691     PISSN: 00221236     EISSN: None     Source Type: Journal    
DOI: 10.1006/jfan.1999.3423     Document Type: Article

References (29)

1. Beals R. On the boundedness of pseudodifferential operators. Comm. Partial Differential Equations. 2:1977;1063-1070.
2. Bony J.-M. Calcul symbolique et propagation des singularités pour les solutions des EDP non linéaires. Ann. Sci. École Norm. Sup. 14:1981;209-246.
3. Boulkhemair A. On canonical transformations of paradifferential operators. Comm. Partial Differential Equations. 18:1993;917-964.
4. 2 précisées pour les opérateurs pseudodifférentiels. C. R. Acad. Sci. Paris Sér. I. 318:1994;445-448.
5. 2 estimates for pseudodifferential operators. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4). 22:1995;155-183.
6. 1, 1. C. R. Acad. Sci. Paris Sér. I. 321:1995;1017-1022.
7. Bourdaud G. Sur les opérateurs pseudodifférentiels à coefficients peu réguliers. 1983;Univ. Paris-Sud, Orsay.
8. Bourdaud G. Une algèbre maximale d'op'erateurs pseudodifférentiels. Comm. Partial Differential Equations. 13:1988;1059-1083.
9. Calderon A. P., Vaillancourt R. A class of bounded pseudodifferential operators. Proc. Nat. Acad. Sci. U.S.A. 69:1972;1185-1187.
10. 2 boundedness of pseudodifferential operators. Proc. Amer. Math. Soc. 61:1976;252-254.
11. Ching C. H. Pseudodifferential operators with non regular symbols. J. Differential Equations. 11:1972;436-447.
12. Coifman R., Meyer Y. Au delà des opérateurs pseudodifférentiels. Astérisque. 57:1978.
13. Cordes H. O. On compactness of commutators of multiplications and convolutions, and boundedness of pseudodifferential operators. J. Funct. Anal. 18:1975;115-131.
14. Folland G. B. Harmonic Analysis in Phase Space. 1989;Princeton Univ. Press, Princeton.
15. Hörmander L. The Weyl calculus of pseudodifferential operators. Comm. Pure Appl. Math. 32:1979;355-443.
16. Hörmander L. Pseudodifferential operators of type (1, 1). Comm. Partial Differential Equations. 13:1988;1085-1111.
17. Hörmander L. Continuity of pseudodifferential operators of type (1, 1). Comm. Partial Differential Equations. 14:1989;231-243.
18. Howe R. Quantum mechanics and partial differential equations. J. Funct. Anal. 38:1980;188-254.
19. 2 boundedness of pseudodifferential operators. Trans. Amer. Math. Soc. 302:1987;55-76.
20. Kato T. The Cauchy problem for quasi-linear symmetric hyperbolic systems. Arch. Rational Mech. Anal. 58:1975;181-205.
21. Kato T. Boundedness of some pseudodifferential operators. Osaka J. Math. 13:1976;1-9.
22. Katznelson Y. An Introduction to Harmonic Analysis. 1976;Dover, New York.
23. Meyer Y. Régularité des solutions d'équations aux dérivées partielles non linéaires. Lecture Notes in Mathematics. 1980;Springer-Verlag, New York/Berlin. p. 293-302.
24. Y. Meyer, Remarques sur un thérème de J. M. Bony, in, Supplemento ai rendiconti del circolo matematico di Palermo, atti del Seminario di Analisis Armonica, Pisa, April 8-17 1980, Vol, II, No.
25. p boundedness of several classes of pseudodifferential operators. Chinese Ann. Math. Ser. B. 5:1984;193-213.
26. Sjöstrand J. An algebra of pseudodifferential operators. Math. Res. Lett. 1:1994;185-192.
27. J. Sjöstrand, Wiener type algebras of pseudodifferential operators, in, Séminaire EDP de l'Ecole Polytechnique, 1994/1995, Exposé No, IV.
28. Taylor M. E. Pseudodifferential Operators and Nonlinear Partial Differential Equations. 1991;Birkhäuser, Boston.
29. Unterberger A. Oscillateur harmonique et opérateurs pseudodifférentiels. Ann. Inst. Fourier. 29:1979;201-221.