Resolvent estimates on symmetric spaces of noncompact type

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Author(s)

Abstract

In this article we prove resolvent estimates for the Laplace-Beltrami operator or more general elliptic Fourier multipliers on symmetric spaces of noncompact type. Then the Kato theory implies time-global smoothing estimates for corresponding dispersive equations, especially the Schrödinger evolution equation. For low-frequency estimates, a pseudo-dimension appears as an upper bound of the order of elliptic Fourier multipliers. A key of the proof is to show a weighted <i>L</i><sup>2</sup>-continuity of the modified Radon transform and fractional integral operators.

Journal

  • Journal of the Mathematical Society of Japan

    Journal of the Mathematical Society of Japan 66(3), 895-926, 2014

    The Mathematical Society of Japan

Codes

  • NII Article ID (NAID)
    130004927749
  • NII NACSIS-CAT ID (NCID)
    AA0070177X
  • Text Lang
    ENG
  • ISSN
    0025-5645
  • NDL Article ID
    025599086
  • NDL Call No.
    Z53-A209
  • Data Source
    NDL  J-STAGE 
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