Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

The $ L\sp 2$-boundedness of pseudodifferential operators


Author: I. L. Hwang
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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [1] A. Calderon and R. Vaillancourt, On the boundedness of pseudodifferential operators, Proc. Nat. Acad. Sci. U.S.A. 69 (1972), 1185-1187. MR 0298480 (45:7532)
  • [2] R. R. Coifman and Y. Meyer, Au delá des opérators pseudo-differentials, Asterisque 57 (1978). MR 518170 (81b:47061)
  • [3] T. Kato, Boundedness of some pseudodifferential operators, Osaka J. Math. 13 (1976), 1-9. MR 0410477 (53:14226)
  • [4] H. Kumano-go, Pseudodifferential operators, MIT Press, Cambridge, Mass., 1981. MR 666870 (84c:35113)
  • [5] R. Beals, On the boundedness of pseudo-differential operators, Comm. Partial Differential Equations 2 (1977), 1063-1070. MR 0477884 (57:17385)
  • [6] H. O. Cordes, On compactness of commutators of multiplications and convolutions, and boundedness of pseudodifferential operators, J. Funct. Anal. 18 (1975), 115-131. MR 0377599 (51:13770)
  • [7] 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.
  • [8] L. Hörmander, The analysis of linear partial differential operators. III, Springer-Verlag, 1985, p. 75 and Chapter 18. MR 781536 (87d:35002a)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 47G05, 35S05

Retrieve articles in all journals with MSC: 47G05, 35S05


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1987-0887496-4
Article copyright: © Copyright 1987 American Mathematical Society

American Mathematical Society