The authors consider the Hodge Laplacian on the Heisenberg group H n , endowed with a left-invariant and U(n) -invariant Riemannian metric. For 0 k 2n 1 , let 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 d 12 k are L p -bounded, for 1 ;
- (3) how to prove a sharp Mihilin-Hoermander multiplier theorem for k , 0 k 2n 1 .
- ISBN13 9781470409395
- Publish Date 30 January 2015
- Publish Status Active
- Publish Country US
- Imprint American Mathematical Society
- Format Paperback
- Pages 91
- Language English