Article

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

D. I. AkramovaSamarkand State University, Samarkand, 140104, UzbekistanIsroil A. IkromovSamarkand State University, Samarkand, 140104, Uzbekistan

Mathematical Notesjournal2021en

ABI

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.

Topics

Quantum chaos and dynamical systems Geometric Analysis and Curvature Flows Mathematical Dynamics and Fractals

Identifiers

DOI: 10.1134/s0001434621050011

Citations and references

Cited by 4 26 references

Metrics — AkademScholar · Coming soon