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 ${\mathcal{M}}_{p,q}({\mathbb{R}}^n),1\le p,q\le \infty ,$ 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.

17 pages