Analysis of the Hodge Laplacian on the Heisenberg Group, Paperback / softback Book

Analysis of the Hodge Laplacian on the Heisenberg Group Paperback / softback

Part of the Memoirs of the American Mathematical Society series

Paperback / softback

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The authors consider the Hodge Laplacian Δ on the Heisenberg group H n , endowed with a left-invariant and U(n) -invariant Riemannian metric.

For 0≤k≤2n 1 , let Δ k denote the Hodge Laplacian restricted to k -forms. In this paper they address three main, related questions:(1) whether the L 2 and L p -Hodge decompositions, 1(2) whether the Riesz transforms dΔ −12 k are L p -bounded, for 1<<∞ ; (3) how to prove a sharp Mihilin-Hörmander multiplier theorem for Δ k , 0≤k≤2n 1 .

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