Fourier Transform of Dini-Lipschitz Functions on the Field of p-Adic Numbers
- 作者: Platonov S.1
-
隶属关系:
- Institute of Mathematics
- 期: 卷 11, 编号 4 (2019)
- 页面: 307-318
- 栏目: Research Articles
- URL: https://journals.rcsi.science/2070-0466/article/view/201299
- DOI: https://doi.org/10.1134/S2070046619040058
- ID: 201299
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详细
Let ℚp be the field of p-adic numbers, a function f(x) belongs to the the Lebesgue class Lρ(ℚp), 1 ρ ≤ 2, and let \(\hat{f}(\xi)\) be the Fourier transform of f. In this paper we give an answer to the next problem: if the function f belongs to the Dini-Lipschitz class DLip(α, β, ρ; ℚp), α > 0, β ∈ ℝ, then for which values of r we can guarantee that \(\hat{f} \in {L^r}(\mathbb{Q}_p)\)? The result is an analogue of one classical theorem of E. Titchmarsh about the Fourier transform of functions from the Lipschitz classes on ℝ.
作者简介
Sergey Platonov
Institute of Mathematics
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Email: ssplatonov@yandex.ru
俄罗斯联邦, Lenina av., 33, Petrozavodsk, 185910