Hörmander multiplier theorem with regularity in modulation spaces. (August 2020) - Huang, Liang; Xu, Chengdan
Abstract: In this paper, we mainly establish the Hörmander type multiplier theorem related to the modulation spaces M 2, p s ( R n ) for all 0 < p ≤ 1 . This extends the result of Tomita (2009) when p = 1 to all the cases 0 < p ≤ 1 . We use the Littlewood–Paley–Stein square functions and atomic decompositions to establish our main result. Furthermore, our method is substantially different from that used in Tomita (2009) when p = 1 .