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