Boundedness of Fourier Multipliers on Fundamental Domains of Lattices

This short paper is an overview of my research about \(L^p\) - \(L^q\) boundedness of Fourier multipliers on fundamental domains of lattices in \(\mathbb {R}^d\) .We start with an outline of Fourier analysis on fundamental domains, then use interpolation techniques to obtain some inequalities and conclude with a Hörmander-type boundedness theorem. At the end, I present some current research perspectives.