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Functional Analysis and Its Applications

, Volume 49, Issue 3, pp 218–221 | Cite as

Integrability of the fourier transforms of measures concentrated on hypersurfaces

  • I. A. Ikromov
Brief Communications
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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 

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Samarkand State UniversityMoscowRussia

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