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On the Hankel transform of functions from Nikol'ski type classes
Integral Transforms and Special Functions ( IF 0.7 ) Pub Date : 2020-11-17 , DOI: 10.1080/10652469.2020.1849184 S. S. Platonov 1
中文翻译:
关于 Nikol'ski 类型类函数的 Hankel 变换
更新日期:2020-11-17
Integral Transforms and Special Functions ( IF 0.7 ) Pub Date : 2020-11-17 , DOI: 10.1080/10652469.2020.1849184 S. S. Platonov 1
Affiliation
Let a function f belong to the Lebesgue class , , and let be the Fourier transform of f. The classical theorem of E. Titchmarsh states that if the function f belongs to the Lipschitz class , , then belongs to the Lebesgue classes for . In this paper we prove an analogue of this result for the the Hankel transform of functions from Nikol'ski type function classes on the half-line .
中文翻译:
关于 Nikol'ski 类型类函数的 Hankel 变换
让函数f属于 Lebesgue 类, , 然后让 是f的傅立叶变换。E. Titchmarsh 的经典定理指出,如果函数f属于 Lipschitz 类, , 然后 属于 Lebesgue 类 为了 . 在本文中,我们证明了半线上来自 Nikol'ski 类型函数类的函数的 Hankel 变换的类似结果.