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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.

UDC: 517.51

Received: 18.08.2013

DOI: 10.4213/faa3190

 English version: Functional Analysis and Its Applications, 2015, 49:3, 218–221

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