Remarks on the Unimodular Fourier Multipliers on α-Modulation Spaces. (17th July 2014) - Zhao, Guoping; Chen, Jiecheng; Guo, Weichao
Abstract : We study the boundedness properties of the Fourier multiplier operatore i μ ( D ) onα -modulation spacesM p, q s, α ( 0 ≤ α < 1 ) and Besov spacesB p, q s ( M p, q s, 1 ) . We improve the conditions for the boundedness of Fourier multipliers with compact supports and for the boundedness ofe i μ ( D ) onM p, q s, α . Ifμ is a radial functionϕ ( | ξ | ) andϕ satisfies some size condition, we obtain the sufficient and necessary conditions for the boundedness ofe i ϕ ( | D | ) betweenM p 1, q 1 s 1, α andM p 2, q 2 s 2, α .