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JOURNALS // Matematicheskie Zametki // Archive

Mat. Zametki, 2021 Volume 109, Issue 5, Pages 643–663 (Mi mzm12744)

This article is cited in 3 papers

Randol Maximal Functions and the Integrability of the Fourier Transform of Measures

D. I. Akramova, I. A. Ikromov

A. Navoi Samarkand State University

Abstract: Estimates of the Fourier transform of charges (measures) concentrated on smooth hypersurfaces are considered. Following M. Sugumoto, three classes of smooth hypersurfaces are defined. Depending on the class, estimates of the Fourier transform of charges are obtained in terms of Randol maximal functions. The obtained estimates are applied to the solution of the integrability problem for the Fourier transform of measures concentrated on some nonconvex hypersurfaces. The sharpness of the obtained estimates is shown.

Keywords: measure, Fourier transform, hypersurface, curvature, integrability.

UDC: 517.518.5

Received: 08.04.2020

DOI: 10.4213/mzm12744


 English version:
Mathematical Notes, 2021, 109:5, 661–678

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© Steklov Math. Inst. of RAS, 2024