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Littlewood-Paley Theory in One and Two Parameters

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ICM-90 Satellite Conference Proceedings

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Abstract

In this talk I shall describe some recent results in Littlewood-Paley theory and their applications to the spectral analysis of certain partial differential operators. I will also sketch a couple of the proofs. As experts in this field know, there are two kinds of Littlewood-Paley theory: “discrete” and “continuous.” For the sake of the non-experts, I will only discuss the discrete theory, even though all of the applications I will mention are from the continuous theory. All of the important ideas are in the discrete case; readers who are interested in the technical details of going over into the continuous setting will all they want (and perhaps more) in [W2] and [W3].

Partially supported under NSF Grant DMS-8811775.

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References

  1. S. Y. A. Chang, J. M. Wilson, T. H. Wolff, “Some weighted norm inequalities concerning the Schrodinger operators,” Comm. Math. Helv. 60 (1985), 217–246.

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  2. C. L. Fefferman, “The uncertainty principle,” Bull Amer. Math.1 Soc. (N.S.) 9 (1983), 129–206.

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  3. J. M. Wilson, “A sharp inequality for the square function,” Duke Math. Journal 55 (1987), 879–887.

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  4. J. M. Wilson, “Weighted norm inequalities for the continuous square function,” Trans. Amer. Math. Soc. 314 (1989), 661–692.

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  5. W3] J. M. Wilson, “Some two-parameter square function inequalities,” to appear in Indiana University Math. Journal.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Vermont, Burlington, Vermont, 05405, USA

    J. M. Wilson

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  1. J. M. Wilson
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Editor information

Editors and Affiliations

  1. Mathematical Institute, Tohoku University, Aobaku, Sendai, Miyagi, 980, Japan

    Satoru Igari

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© 1991 Springer-Verlag Tokyo

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Wilson, J.M. (1991). Littlewood-Paley Theory in One and Two Parameters. In: Igari, S. (eds) ICM-90 Satellite Conference Proceedings. Springer, Tokyo. https://doi.org/10.1007/978-4-431-68168-7_19

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  • DOI: https://doi.org/10.1007/978-4-431-68168-7_19

  • Publisher Name: Springer, Tokyo

  • Print ISBN: 978-4-431-70084-5

  • Online ISBN: 978-4-431-68168-7

  • eBook Packages: Springer Book Archive

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