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arXiv · 1303.5047

Remarks on functional calculus for perturbed first order Dirac operators

Pascal Auscher·Sebastian Stahlhut
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Abstract

We make some remarks on earlier works on $R-$bisectoriality in $L^p$ of perturbed first order differential operators by Hytönen, McIntosh and Portal. They have shown that this is equivalent to bounded holomorphic functional calculus in $L^p$ for $p$ in any open interval when suitable hypotheses are made. Hytönen and McIntosh then showed that $R$-bisectoriality in $L^p$ at one value of $p$ can be extrapolated in a neighborhood of $p$. We give a different proof of this extrapolation and observe that the first proof has impact on the splitting of the space by the kernel and range.

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Pascal Auscher, Sebastian Stahlhut. 2013-03-20. Remarks on functional calculus for perturbed first order Dirac operators. https://arxiv.org/abs/1303.5047

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