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

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

2011-09-02

arxiv.org/abs/1109.0429v1

Mathematics

Classical Analysis and ODEs

Scientific paper

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 $\mathcal{L}$.

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