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On the boundedness of pseudo-differential operators


Author: Chin Hung Ching
Journal: Proc. Amer. Math. Soc. 41 (1973), 179-182
MSC: Primary 47G05; Secondary 35S05
DOI: https://doi.org/10.1090/S0002-9939-1973-0320823-0
MathSciNet review: 0320823
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Abstract: In this note, we use the sequence version of Cotlar's lemma and a partition of unity to give a proof of the $ {L^2}$-boundedness of a class of pseudo-differential operators.


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

  • [1] A. P. Calderón and R. Vaillencourt, On the boundedness of pseudo-differential operators, J. Math. Soc. Japan. 23 (1971), 374-378. MR 44 #2096. MR 0284872 (44:2096)
  • [2] A. W. Knapp and E. M. Stein, Singular integrals and the principal series, Proc. Nat. Acad. Sci. U.S.A. 63 (1969), 281-284; ibid. 66 (1970), 13-17. MR 41 #8588. MR 0263989 (41:8588)
  • [3] J. Kohn and L. Nirenberg, An algebra of pseudo-differential operators, Comm. Pure Appl. Math. 18 (1965), 269-305. MR 31 #636. MR 0176362 (31:636)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1973-0320823-0
Keywords: Pseudo-differential operators, symbol, bounded operator, Cotlar lemma
Article copyright: © Copyright 1973 American Mathematical Society

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