Lᵖ-spectral multipliers for the Hodge Laplacian acting on 1-forms on the Heisenberg group

الأصل · EN

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-Hörmander multiplier on the positive half-line, with L²-order of smoothness greater than n+1/2, then m(Δ₁) is Lᵖ-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.