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L-spectral Multipliers for the Hodge Laplacian Acting on 1-forms on the Heisenberg Group
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 ter...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1981
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1981.95.143