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

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 $0\leq\delta<\rho\leq1.$