We prove that, if Δ_1 is the Hodge Laplacian acting on differential 1-forms on the (2n+1)-dimensional Heisenberg group, and if m is a Mihlin-Hörmander multiplier on the positive half-line, with L^2-order of smoothness greater than n+1/2, then m(Δ_1) is L^p-bounded for 1 < p < infinity. Our approach leads to an explicit description of the spectral decomposition of Δ_1 on the space of L^2-forms in terms of the spectral analysis of the sub-Laplacian L and the central derivative T, acting on scalar-valued functions.

L^p-spectral multipliers for the Hodge Laplacian acting on 1-forms on the Heisenberg group / D. Müller, M. M. Peloso, F. Ricci. - In: GEOMETRIC AND FUNCTIONAL ANALYSIS. - ISSN 1016-443X. - 17:3(2007), pp. 852-886.

L^p-spectral multipliers for the Hodge Laplacian acting on 1-forms on the Heisenberg group

M. M. Peloso
Secondo
;
2007

Abstract

We prove that, if Δ_1 is the Hodge Laplacian acting on differential 1-forms on the (2n+1)-dimensional Heisenberg group, and if m is a Mihlin-Hörmander multiplier on the positive half-line, with L^2-order of smoothness greater than n+1/2, then m(Δ_1) is L^p-bounded for 1 < p < infinity. Our approach leads to an explicit description of the spectral decomposition of Δ_1 on the space of L^2-forms in terms of the spectral analysis of the sub-Laplacian L and the central derivative T, acting on scalar-valued functions.
Heisenberg group ; Hodge Laplacian ; spectral multipliers ; sub-Laplacian
Settore MAT/05 - Analisi Matematica
2007
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/37133
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