Fourier multipliers between weighted anisotropic function spaces. I: Besov spaces (Q1924304)

The author characterized the classes \({\mathbf M}(B^{s_0}_{p_0,q_0}(\omega_0),B^{s_1}_{p_1,q_1}(\omega_1))\) of Fourier multipliers between weighted anisotropic Besov spaces \(B^{s_0}_{p_0,q_0}(\omega_0)\) and \(B^{s_1}_{p_1,q_1}(\omega_1),\) where \(p_0\leq 1\) and \(\omega_0,\;\omega_1\) are weight functions of polynomial growth. The author obtained these results by a discrete characterization of these function spaces akin to the \(\varphi\)-transform of Frazier and Jawerth. The author's results generalize the known results of Bui, Johnson, Peetre and others. [See also the review of Part II below].