Fourier Multipliers and Littlewood-Paley For Modulation Spaces

Abstract: In this paper we have studied Fourier multipliers and Littlewood-Paley square functions in the context of modulation spaces. We have also proved that any bounded linear operator from modulation space $\mathcal{M}_{p,q}(\R^n), 1\leq p,q\leq \infty,$ into itself possesses an $l_2-$valued extension. This is an analogue of a well known result due to Marcinkiewicz and Zygmund on classical $L^p-$spaces.