Hörmander-type theorems on unimodular multipliers and applications to modulation spaces

Abstract

In this article, for the unimodular multipliers $e^{i\mu \left(D\right)}$, we establish two Hörmander-type multiplier theorems by assuming conditions on their phase functions $\mu$. As applications, we obtain two multiplier theorems particularly fitting for the modulation spaces, thus allowing us to extend and improve some known results.