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arXiv · 1109.0429

Multipliers and imaginary powers of the schr\"odinger operators characterizing UMD Banach spaces

J. J. Betancor·R. Crescimbeni·J. C. FariÑa·And L. RodrÍguez-Mesa
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Abstract

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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J. J. Betancor, R. Crescimbeni, J. C. FariÑa, And L. RodrÍguez-Mesa. 2011-09-02. Multipliers and imaginary powers of the schr\"odinger operators characterizing UMD Banach spaces. https://arxiv.org/abs/1109.0429

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