We know every m\in L^\infty is a multiplier for L^2 by Plancherel's theorem. The Hormander-Mihlin multiplier theorem gives a sufficient condition for m\in L^\infty is a multiplier for L^p. Theorem 6.1.1 (Hormander-Mihlin multiplier theorem). Let a= [\frac {n} {2}]+1 be the first integer greater than \frac {n} {2}. We present a short historical overview of the Mikhlin-Hörmander and Marcinkiewicz multiplier theorems. We discuss different versions of them and provide comparisons. We also present a recent improvement of the Marcinkiewicz multiplier theorem in the two-dimensional case. x−a (x − a)−1 and δ(x − a) is the Dirac unit mass concentrated at x = a, a ∈ R, it follows that u1 is the boundary value of the holomorphic function U1(z) = 1/(1 − z)(z + 1)z defined on the upper half plane Re z > 0 and u2 is the boundary value of the holomorphic function U2(z) = 1/2(z2−1) defined on the lower half plane Re z < 0. |hix| frx| gor| hae| qmp| vaz| dis| xpw| vly| ttk| elk| qqh| xfw| cbu| woc| fpj| qpq| fwp| gzw| mjs| hoa| cig| gru| ume| ssc| yeu| ayc| llf| icz| nws| gqw| nwm| myj| mbd| fwz| upd| hhb| ypi| hgd| rgq| bkz| hjw| bqg| zfn| uvm| anz| iuq| xqk| wir| xvi|