Title: An (n + 1)– fold Marcinkiewicz multiplier theorem on the Heisenberg group
Abstract: We prove a Marcinkiewicz-type multiplier theorem on the Heisenberg group: for 1 < p < ∞, we establish the boundedness on L p (ℍ n ) of spectral multipliers m (ℒ 1 ,…,ℒ n , iT ) of the n partial sub-Laplacians ℒ 1 ,…,ℒ n and iT , where m satisfies an ( n + l)-fold Marcinkiewicz-type condition. We also establish regularity and cancellation conditions which the convolution kernels of these Marcinkiewicz multipliers m (ℒ 1 ,…,ℒ n , iT ) satisfy.