Mapping properties of Fourier transforms, II

TL;DR

This paper continues the study of Fourier transform mapping properties, focusing on continuous and compact mappings between weighted function spaces on Euclidean space, extending previous work with a consistent notation.

Contribution

It advances the understanding of Fourier transform mappings between weighted function spaces, specifically analyzing conditions for continuity and compactness.

Findings

Characterization of continuous Fourier transform mappings

Criteria for compactness of Fourier transform operators

Extension of previous results to broader weighted spaces

Abstract

This is the direct continuation of the paper "Mapping properties of Fourier transforms" (arXiv:2112.04896) using the same notation as there without further explanations. It deals with continuous and compact mappings of the Fourier transform $F$ between some weighted function spaces on $\mathbb{R}^n$.