نبذة مختصرة : International audience ; Kazaniecki and Wojciechowskiproved in 2013 that every Fourier multiplier on $\dot{W}^{1,1}\left( \mathbb{R}^{d}\right) $ is a bounded continuous function on $\mathbb{R}^{d}$. This is a generalization of a previous result of Bonami and Poornima (1987)concerning homogeneous multipliers of degree zero. We further generalize the resultof Kazaniecki and Wojciechowski. We prove that, given an integer $l\geq1$,every multiplier on $\dot{W}^{l,1}\left( \mathbb{R}^{d}\right) $ or on $\dot{W}^{l,\infty}\left( \mathbb{R}^{d}\right) $ is a bounded continuous functionon $\mathbb{R}^{d}$. We obtain these results via a substantial simplification of the Riesz products technique used by Kazaniecki and Wojciechowski.
Processing Request
No Comments.