%0 Journal Article
%T Multipliers and imaginary powers of the schr£¿dinger operators characterizing UMD Banach spaces
%A J. J. Betancor
%A R. Crescimbeni
%A J. C. Fari£¿a
%A And L. Rodr¨ªguez-Mesa
%J Mathematics
%D 2011
%I arXiv
%X 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 $\mathcal{L}$.
%U http://arxiv.org/abs/1109.0429v1