The $L^ 2$-boundedness of pseudodifferential operators
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- by I. L. Hwang PDF
- Trans. Amer. Math. Soc. 302 (1987), 55-76 Request permission
Abstract:
We give a new proof of the Calderon-Vaillancourt theorem. We also obtain the ${L^2}$-continuity of $a(x,D)$ if its symbol $a(x,\xi )$ satisfies some suitable conditions.References
- Alberto-P. Calderón and Rémi Vaillancourt, A class of bounded pseudo-differential operators, Proc. Nat. Acad. Sci. U.S.A. 69 (1972), 1185–1187. MR 298480, DOI 10.1073/pnas.69.5.1185
- Ronald R. Coifman and Yves Meyer, Au delà des opérateurs pseudo-différentiels, Astérisque, vol. 57, Société Mathématique de France, Paris, 1978 (French). With an English summary. MR 518170
- Tosio Kato, Boundedness of some pseudo-differential operators, Osaka Math. J. 13 (1976), no. 1, 1–9. MR 410477
- Hitoshi Kumano-go, Pseudodifferential operators, MIT Press, Cambridge, Mass.-London, 1981. Translated from the Japanese by the author, Rémi Vaillancourt and Michihiro Nagase. MR 666870
- Richard Beals, On the boundedness of pseudo-differential operators, Comm. Partial Differential Equations 2 (1977), no. 10, 1063–1070. MR 477884, DOI 10.1080/03605307708820055
- H. O. Cordes, On compactness of commutators of multiplications and convolutions, and boundedness of pseudodifferential operators, J. Functional Analysis 18 (1975), 115–131. MR 377599, DOI 10.1016/0022-1236(75)90020-8 T. Muramato and M. Nagase, ${L^2}$-boundedness of pseudodifferential operators with non-regular symbols, Canad. Math. Soc. Conf. Proc., Vol. 1, Amer. Math. Soc., Providence, R.I., 1981, p. 138.
- Lars Hörmander, The analysis of linear partial differential operators. III, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 274, Springer-Verlag, Berlin, 1985. Pseudodifferential operators. MR 781536
Additional Information
- © Copyright 1987 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 302 (1987), 55-76
- MSC: Primary 47G05; Secondary 35S05
- DOI: https://doi.org/10.1090/S0002-9947-1987-0887496-4
- MathSciNet review: 887496