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

Abstract

In this paper we establish $L^p$-boundedness properties for Laplace type transform spectral multipliers associated with the Schrödinger 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 $\mathcal{L}$.

References in corpus (1)

• $L^p$-boundeness properties of variation operators in the Schrodinger setting