$L^p$-bounds for Fourier integral operators on the torus

TL;DR

This paper studies the boundedness of periodic Fourier integral operators with limited regularity symbols on $L^p$ spaces over the torus, extending understanding of their mapping properties in harmonic analysis.

Contribution

It provides new $L^p$ bounds for Fourier integral operators on the torus with symbols of limited regularity, advancing the theory of periodic Fourier analysis.

Findings

Established $L^p$-boundedness for a class of periodic Fourier integral operators.

Extended previous results to symbols with limited regularity.

Enhanced understanding of operator behavior on toroidal domains.

Abstract

In this paper we investigate the mapping properties of periodic Fourier integral operators in $L^p(\mathbb{T}^n)$-spaces. The operators considered are associated to periodic symbols (with limited regularity) in the sense of Ruzhansky and Turunen.