Let G = NA,where N is a stratified group and A =R acts on N via automorphic dilations. Homogeneous sub-Laplacians on N and A can be lifted to left-invariant operators on G, and their sum is a sub-Laplacian L on G. We prove a theorem of Mihlin–H¨ormander type for spectral multipliers of L.The proof of the theorem hinges on a Calder´on–Zygmund theory adapted to a sub-Riemannian structure of G and on L1-estimates of the gradient of the heat kernelassociated to the sub-Laplacian.

Spectral multipliers for sub-Laplacians on solvable extensions of stratified groups / Martini, Alessio; Ottazzi, Alessandro; Vallarino, Maria. - In: JOURNAL D'ANALYSE MATHEMATIQUE. - ISSN 0021-7670. - STAMPA. - 136:1(2018), pp. 357-397. [10.1007/s11854-018-0063-6]

Spectral multipliers for sub-Laplacians on solvable extensions of stratified groups

Martini, Alessio;Vallarino, Maria
2018

Abstract

Let G = NA,where N is a stratified group and A =R acts on N via automorphic dilations. Homogeneous sub-Laplacians on N and A can be lifted to left-invariant operators on G, and their sum is a sub-Laplacian L on G. We prove a theorem of Mihlin–H¨ormander type for spectral multipliers of L.The proof of the theorem hinges on a Calder´on–Zygmund theory adapted to a sub-Riemannian structure of G and on L1-estimates of the gradient of the heat kernelassociated to the sub-Laplacian.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11583/2721538
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