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**Kalf, Hubert; Okaji, Takashi and Yamada, Osanobu (2019): Explicit uniform bounds on integrals of Bessel functions and trace theorems for Fourier transforms. In: Mathematische Nachrichten, Vol. 292, No. 1: pp. 106-120**

**Full text not available from 'Open Access LMU'.**

## 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 L-2 restrictions of Fourier transforms onto spheres in R-n which are independent of the radius of the sphere. For more special weights these restrictions are shown to be Holder continuous with a Holder 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.

Item Type: | Journal article |
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Faculties: | Mathematics, Computer Science and Statistics > Mathematics |

Subjects: | 500 Science > 510 Mathematics |

ISSN: | 0025-584X |

Language: | English |

Item ID: | 82417 |

Date Deposited: | 15. Dec 2021, 15:01 |

Last Modified: | 15. Dec 2021, 15:01 |