Analysis of the Hodge Laplacian on the Heisenberg Group (Memoirs of the American Mathematical Society)
Analysis of the Hodge Laplacian on the Heisenberg Group (Memoirs of the American Mathematical Society) by Detlef Muller
English | 2014 | ISBN: 1470409399 | 91 Pages | PDF | 869.47 KB
English | 2014 | ISBN: 1470409399 | 91 Pages | PDF | 869.47 KB
The authors consider the Hodge Laplacian DELTA on the Heisenberg group H n , endowed with a left-invariant and U(n) -invariant Riemannian metric. For 0<=k<=2n 1 , let DELTA 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 , hold on H n;*(2) whether the Riesz transforms dDELTA -12 k are L p -bounded, for 1" ; *(3) how to prove a sharp Mihilin-Hormander multiplier theorem for DELTA k , 0<=k<=2n 1 .