Pitt inequalities and restriction theorems for the Fourier transform

TL;DR

This paper establishes new Pitt inequalities, Riemann-Lebesgue estimates, and uncertainty principles for the Fourier transform, utilizing weighted restriction inequalities on the sphere, applicable to both radial and non-radial weights.

Contribution

It introduces novel Pitt inequalities and restriction theorems for the Fourier transform, expanding the understanding of weighted inequalities and uncertainty principles.

Findings

New Pitt inequalities for Fourier transforms with weights

Weighted restriction inequalities on the sphere

Enhanced Riemann-Lebesgue estimates and uncertainty principles

Abstract

We prove new Pitt inequalities for the Fourier transforms with radial and non-radial weights using weighted restriction inequalities for the Fourier transform on the sphere. We also prove new Riemann-Lebesgue estimates and versions of the uncertainty principle for the Fourier transform.