Analysis of the Hodge Laplacian on the Heisenberg group
Author(s)
Bibliographic Information
Analysis of the Hodge Laplacian on the Heisenberg group
（Memoirs of the American Mathematical Society, no. 1095）
American Mathematical Society, [2015], c2014
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Note
"January 2015, volume 233, number 1095 (first of 6 numbers)."
Includes bibliographical references (p. 89-91)
Description and Table of Contents
Description
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 .
Table of Contents
Introduction
Differential forms and the Hodge Laplacian on Hn
Bargmann representations and sections of homogeneous bundles
Cores, domains and self-adjoint extensions
First properties of Dk exact and closed forms
A decomposition of L2 Lkh related to the ¶ and ¶ complexes
Intertwining operators and different scalar forms for Dk
Unitary intertwining operators and projections
Decomposition of L2 Lk
Lp-multipliers
Decomposition of LpLk and boundedness of the Riesz transforms
Applications
Appendix
Bibliography
by "Nielsen BookData"