Detlef Müller, Marco M. Peloso, Fulvio Ricci:

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

We prove that, if Δ₁ is the Hodge Laplacian acting on differential 1-forms on the (2n+1)-dimensional Heisenberg group, and if m is a Mihlin-Hørmander multiplier on the positive half-line, with L²-order of smoothness greater than n+1/2, then m(Δ₁) is L^p-bounded for 1 < p < ∞. Our approach leads to an explicit description of the spectral decomposition of Δ₁ on the space of L²-forms in terms of the spectral analysis of the sub-Laplacian L and the central derivative T, acting on scalar-valued functions.

Electronic Print: Front for the Mathematics ArXiv

Mathematics Subject Classification (1991): 43A80, 42B15

Bibliographical note: erscheint in GAFA

Mail an Jens Burmeister

[Thu Feb 19 18:56:36 2009]

Impressum