V. V. Lebedev, “On the Fourier Transform of the Characteristic Functions of Domains with $C^1$ Boundary”, Funktsional. Anal. i Prilozhen., 47:1 (2013), 33–46; Funct. Anal. Appl., 47:1 (2013), 27

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Funktsional'nyi Analiz i ego Prilozheniya, 2013, Volume 47, Issue 1, Pages 33–46
DOI: https://doi.org/10.4213/faa3093 (Mi faa3093)

This article is cited in 7 scientific papers (total in 7 papers)

On the Fourier Transform of the Characteristic Functions of Domains with

C^{1}

$C^1$ Boundary

V. V. Lebedev

Moscow State Institute of Electronics and Mathematics — Higher School of Economics

Full-text PDF (220 kB) Citations (7)

References:

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DOI: https://doi.org/10.4213/faa3093

Abstract: We consider domains

$D\subseteq\mathbb R^n$ with

$C^1$ boundary and study the following question: For what domains

$D$ does the Fourier transform

$\widehat{1_D}$ of the characteristic function

$1_D$ belong to

$L^p(\mathbb R^n)$ ?

Keywords: harmonic analysis, domain with smooth boundary, Fourier transform of a characteristic function.

Received: 20.05.2011

English version:
Functional Analysis and Its Applications, 2013, Volume 47, Issue 1, Pages 27–37
DOI: https://doi.org/10.1007/s10688-013-0004-1

Bibliographic databases:

Document Type: Article

UDC: 517.51

Language: Russian

Citation: V. V. Lebedev, “On the Fourier Transform of the Characteristic Functions of Domains with

$C^1$ Boundary”, Funktsional. Anal. i Prilozhen., 47:1 (2013), 33–46; Funct. Anal. Appl., 47:1 (2013), 27–37

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/faa3093

https://doi.org/10.4213/faa3093

https://www.mathnet.ru/eng/faa/v47/i1/p33

This publication is cited in the following 7 articles:

I. A. Ikromov, D. Ikromova, “Sharp $L^p$-Estimates for the Fourier Transform of Surface Measures”, Math. Notes, 115:1 (2024), 44–65
I. A. Ikromov, A. R. Safarov, A. T. Absalamov, “Ob otsenke trigonometricheskikh integralov s kvadratichnoi fazoi”, Chebyshevskii sb., 25:1 (2024), 52–61
Isroil A. Ikromov, Akbar R. Safarov, Akmal T. Absalamov, “On the convergence exponent of the special integral of the tarry problem for a quadratic polynomial”, Zhurn. SFU. Ser. Matem. i fiz., 16:4 (2023), 488–497
D. I. Akramova, I. A. Ikromov, “Randol Maximal Functions and the Integrability of the Fourier Transform of Measures”, Math. Notes, 109:5 (2021), 661–678
H. Ko, S. Lee, “Fourier transform and regularity of characteristic functions”, Proc. Amer. Math. Soc., 145:3 (2017), 1097–1107
F. Avram, N. Leonenko, L. Sakhno, “Limit theorems for additive functionals of stationary fields, under integrability assumptions on the higher order spectral densities”, Stochastic Process. Appl., 125:4 (2015), 1629–1652
I. A. Ikromov, “Integrability of the Fourier Transforms of Measures Concentrated on Hypersurfaces”, Funct. Anal. Appl., 49:3 (2015), 218–221

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Functional Analysis and Its Applications

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