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

Hubert Kalf, Takashi Okaji and Osanobu Yamada

Mathematische Nachrichten, 2019, vol. 292, issue 1, 106-120

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.

Date: 2019
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https://doi.org/10.1002/mana.201700326

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