On the boundedness of periodic pseudo-differential operators

TL;DR

This paper studies the boundedness of specific periodic pseudo-differential operators on L^p spaces, focusing on symbols with limited regularity on the torus and integer lattice.

Contribution

It provides new results on the L^p-boundedness of periodic pseudo-differential operators with symbols of limited regularity.

Findings

Established L^p-boundedness for certain classes of operators

Extended previous results to symbols with lower regularity

Analyzed operators on the torus and integer lattice

Abstract

In this paper we investigate the $L^p$-boundedness of certain classes of periodic pseudo-differential operators. The operators considered arise from the study of symbols on $\mathbb{T}^n\times\mathbb{Z}^n$ with limited regularity.