LP -bound for the Fourier Transform of Surface-Carried Measures Supported on Hypersurfaces with D∞ Type Singularities

Abstract

Received 02.02.2020, received in revised form 06.03.2020, accepted 06.04.2020 Abstract. Estimate for Fourier transform of surface-carried measures supported on non-convex surfaces of three-dimensional Euclidean space is considered in this paper.The exact convergence exponent was found wherein the Fourier transform of measures is integrable in tree-dimensional space. This result gives an answer to the question posed by Erdösh and Salmhofer.