On the boundedness of periodic Fourier integral operators in Lebesgue spaces with variable exponent

TL;DR

This paper studies the boundedness of periodic Fourier integral operators with symbols in Hörmander classes on Lebesgue spaces with variable exponents on the torus, extending classical results to variable exponent settings.

Contribution

It establishes boundedness criteria for these operators in variable exponent Lebesgue spaces, a novel extension of classical Fourier analysis results.

Findings

Boundedness of operators in variable exponent spaces established

Conditions on symbols for boundedness derived

Extension of classical Fourier integral operator theory to variable exponents

Abstract

The aim of this paper is to investigate the boundedness of periodic Fourier integral operators in Lebesgue spaces with variable exponent $L^{p(\cdot)}$ on the $n$-dimensional torus. We deal with operators of type $(\rho, \delta)$ which symbols belong to the H\"{o}rmander class $S^{m}_{\rho, \delta}(\mathbb{T}^{n}\times\mathbb{Z}^{n})$ for $0\leq\delta<\rho\leq1.$