Abstract: Fourier multiplier operators are among the most important operators in mathematical analysis due to their wide range of applications. In this talk, we consider a class of oscillatory multipliers of the form $e^{it|\xi |}(1+|\xi |{)}^{-b}$, with $t>0$ and $b\in \mathbb{R}$, and investigate their boundedness properties on $\beta$-dimensional spaces of measures that lie between the Hardy space $H^1({\mathbb{R}}^n)$ and the space of finite Radon measures. Our estimates give a refinement of known estimates of Miyachi and Peral for the Hardy space. We also discuss an application of these estimates to the solution of the wave equation with measure data. This talk is based on a joint work with Daniel Spector.

 

Organizers: Harry Richman (NCTS), Wille Liu (Academia Sinica)