On the Hörmander multiplier theorem and modulation spaces

Abstract

It is known that the Sobolev space $L_s^2$ with $s>n/2$ appeared in the Hörmander multiplier theorem can be replaced by the Besov space $B_{n/2}^{2,1}$. On the other hand, the Besov space $B_{n/2}^{2,1}$ is continuously embedded in the modulation space $M_0^{2,1}$. In this paper, we consider the problem whether we can replace $B_{n/2}^{2,1}$ by $M_0^{2,1}$.

References in corpus (1)

• A Beurling-Helson type theorem for modulation spaces