Multipliers and imaginary powers of the schr\"odinger operators   characterizing UMD Banach spaces
  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 $\mathcal{L}$. 
J.J. Betancor, R. Crescimbeni, J.C. Fari\~Na, And L. Rodr\'Iguez-Mesa
math.CA