Denote $S$ as the space of Schwartz functions, for $v\in S'$, the space of tempered distributions, define an operator $T_v:f\in S \to f*v$. Then space of Hormander Multipliers $M^{p,q}$ can be defined as $\{ v\in S': \|T_v\|_{L^p\to L^q}<\infty \}$.

Do we know some results on the characterization of $M^{p,q}$, when $p < q$?