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J. Sib. Fed. Univ. Math. Phys., 2020, Volume 13, Issue 3, Pages 350–359 (Mi jsfu844)  

$L^p$-bound for the Fourier transform of surface-carried measures supported on hypersurfaces with $D_\infty$ type singularities

Nigina A. Soleeva

Samarkand State University, Samarkand, Uzbekistan

Abstract: Estimate for Fourier transform of surface-carried measures supported on non-convex surfaces of three-dimensional Euclidean space is considered in this paper.The exact convergence exponent was found wherein the Fourier transform of measures is integrable in tree-dimensional space. This result gives an answer to the question posed by Erdösh and Salmhofer.

Keywords: Fourier transform, oscillatory integral, surface-carried measure.

DOI: https://doi.org/10.17516/1997-1397-2020-13-3-350-359

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UDC: 517.518
Received: 02.02.2020
Received in revised form: 06.03.2020
Accepted: 06.04.2020
Language:

Citation: Nigina A. Soleeva, “$L^p$-bound for the Fourier transform of surface-carried measures supported on hypersurfaces with $D_\infty$ type singularities”, J. Sib. Fed. Univ. Math. Phys., 13:3 (2020), 350–359

Citation in format AMSBIB
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\by Nigina~A.~Soleeva
\paper $L^p$-bound for the Fourier transform of surface-carried measures supported on hypersurfaces with $D_\infty$ type singularities
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2020
\vol 13
\issue 3
\pages 350--359
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\crossref{https://doi.org/10.17516/1997-1397-2020-13-3-350-359}
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  • Журнал Сибирского федерального университета. Серия "Математика и физика"
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