Fourier multipliers for Sobolev spaces on the Heisenberg group

Abstract

A b s t r a c t . In this paper, it is shown that the class of right Fourier multipliers for the Sobolev space W k,p (H n ) coincides with the class of right Fourier multipliers forand L is the sublaplacian on H n . This proof is based on the Calderon-Zygmund theory on the Heisenberg group. It is also shown that when p = 1, the class of right multipliers for the Sobolev space W k,1 (H n ) coincides with the dual space of the projective tensor product of two function spaces.

Homogeneous Fourier and Weyl multipliers on Sobolev spaces related to the Heisenberg group

“…These Sobolev spaces are defined in terms of certain left invariant vector fields which are the counter parts of partial derivatives on R n . It has been proved in [8] that the class of Fourier multipliers on the Sobolev spaces W N,p (H n ) coincides with the class of Fourier multipliers on L p (H n ) for 1 < p < ∞. They have also obtained an abstract characterisation of Fourier multipliers on W N,1 (H n ).…”