Sub-Laplacians of holomorphic $L^{p}$-type on exponential Lie groups
Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 13 (2002) no. 3-4, pp. 259-270.

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In this survey article, I shall give an overview on some recent developments concerning the $L^{p}$-functional calculus for sub-Laplacians on exponential solvable Lie groups. In particular, I shall give an outline on some recent joint work with W. Hebisch and J. Ludwig on sub-Laplacians which are of holomorphic $L^{p}$-type, in the sense that every $L^{p}$-spectral multiplier for $p \neq 2$ will be holomorphic in some domain. 
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Detlef, Müller. Sub-Laplacians of holomorphic $L^{p}$-type on exponential Lie groups. Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 13 (2002) no. 3-4, pp. 259-270. https://geodesic-test.mathdoc.fr/item/AANLMA_2002_9_13_3-4_a7/