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Explicit uniform bounds on integrals of Bessel functions and trace theorems for Fourier transforms

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  • Hubert Kalf
  • Takashi Okaji
  • Osanobu Yamada

Abstract

Explicit and partly sharp estimates are given of integrals over the square of Bessel functions with an integrable weight which can be singular at the origin. They are uniform with respect to the order of the Bessel functions and provide explicit bounds for some smoothing estimates as well as for the L2 restrictions of Fourier transforms onto spheres in Rn which are independent of the radius of the sphere. For more special weights these restrictions are shown to be Hölder continuous with a Hölder constant having this independence as well. To illustrate the use of these results a uniform resolvent estimate of the free Dirac operator with mass m≥0 in dimensions n≥2 is derived.

Suggested Citation

  • Hubert Kalf & Takashi Okaji & Osanobu Yamada, 2019. "Explicit uniform bounds on integrals of Bessel functions and trace theorems for Fourier transforms," Mathematische Nachrichten, Wiley Blackwell, vol. 292(1), pages 106-120, January.
    • Handle: RePEc:bla:mathna:v:292:y:2019:i:1:p:106-120
    DOI: 10.1002/mana.201700326
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