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

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

2005-08-27

arxiv.org/abs/math/0508543v1

Mathematics

Classical Analysis and ODEs

34 pages

Scientific paper

We prove that, if \Delta_1 is the Hodge Laplacian acting on differential 1-forms on the (2n+1)-dimensional Heisenberg group, and if m is a Mihlin-H\"ormander multiplier on the positive half-line, with L^2-order of smoothness greater than n+1/2, then m(\Delta_1) is L^p-bounded for 1

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