标题： 乘子和薛定谔算子的虚数次幂表征UMD巴拿赫空间 显示英文标题

标题： Multipliers and imaginary powers of the schrödinger operators characterizing UMD Banach spaces

摘要： 在本文中，我们建立了与薛定谔算子$\mathcal{L}=-\Delta +V$相关的拉普拉斯型变换谱乘子的$L^p$有界性性质。我们为此类乘子获得了逐点表示作为主值积分算子。我们还通过$\mathcal{L}$的虚数次幂$\mathcal{L}^{i\gamma}$,$\gamma \in \mathbb{R}$的$L^p$有界性来表征 UMD Banach 空间。 显示英文摘要

摘要： In this paper we establish $L^p$-boundedness properties for Laplace type transform spectral multipliers associated with the Schr\"odinger operator $\mathcal{L}=-\Delta +V$. We obtain for this type of multipliers pointwise representation as principal value integral operators. We also characterize the UMD Banach spaces in terms of the $L^p$-boundedness of the imaginary powers $\mathcal{L}^{i\gamma}$, $\gamma \in \mathbb{R}$, of $\mathcal{L}$.