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Funktsional. Anal. i Prilozhen., 2015, Volume 49, Issue 3, Pages 74–79 (Mi faa3190)  

Brief communications

Integrability of the Fourier Transforms of Measures Concentrated on Hypersurfaces

I. A. Ikromov

A. Navoi Samarkand State University

Abstract: This paper considers estimates for the Fourier transforms of signed measures concentrated on families of hypersurfaces. A theorem about the integrability of Randol-type maximal functions related to a certain class of nonconvex hypersurfaces is presented. The results are applied to study the integrability of the Fourier transforms of signed measures concentrated on certain hypersurfaces. In a special case, the exact integrability exponent of the Fourier transforms of measures is specified. The results improve a recent theorem of L. Erdős and M. Salmhofer.

Keywords: asymptotics, Fourier transforms, integrability, curvature

Funding Agency Grant Number
Исполнительный комитет по координации науки и технологий при КМ Республики Узбекистан Ф-4-17


DOI: https://doi.org/10.4213/faa3190

Full text: PDF file (191 kB)
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English version:
Functional Analysis and Its Applications, 2015, 49:3, 218–221

Bibliographic databases:

UDC: 517.51
Received: 18.08.2013

Citation: I. A. Ikromov, “Integrability of the Fourier Transforms of Measures Concentrated on Hypersurfaces”, Funktsional. Anal. i Prilozhen., 49:3 (2015), 74–79; Funct. Anal. Appl., 49:3 (2015), 218–221

Citation in format AMSBIB
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