Explicit uniform bounds on integrals of Bessel functions and trace theorems for Fourier transforms
Explicit uniform bounds on integrals of Bessel functions and trace theorems for Fourier transforms
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贝塞尔函数积分的显式一致界限和傅立叶变换的迹定理
DOI：
10.1002/mana.201700326
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发表时间：
2019
影响因子：
1
通讯作者：
Takashi Okaji and Osanobu Yamada
中科院分区：
文献类型：
--
作者：
Hubert Kalf;Takashi Okaji and Osanobu Yamada
给出了具有可积权且原点奇异的贝塞尔函数平方上积分的显式和部分精确估计。它们关于Bessel函数的阶是一致的，并为某些光滑估计以及与球面半径无关的球面上Fourier变换的L2限制提供了明确的界.对于更特殊的权重，这些限制被证明是Hölder连续的，Hölder常数也具有这种独立性。为了说明这些结果的使用，一个统一的预解估计的自由狄拉克运营商与质量的尺寸。
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 theL2restrictions of Fourier transforms onto spheres in 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 in dimensions is derived.