Hörmander multiplier theorem with regularity in modulation spaces. (August 2020)

• Record Type: Journal Article
• Authors: Huang, Liang; Xu, Chengdan
• Is Part Of: Nonlinear analysis. Volume 197(2020)
• Publication Date: 2020-08
• Subjects: Modulation space -- Hardy space -- Fourier multiplier -- Littlewood–Paley–Stein square functions; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2020.111789
• Languages: English
• ISSNs: 0362-546X

Abstract

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 .