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

摘要

Inspired by the work of A. Bonami and S. Poornima that a non-constant function which is homogeneous of degree 0 cannot be a Fourier multiplier on homogeneous Sobolev spaces, we establish analogous results for Fourier multipliers on the Heisenberg group Hnand Weyl multipliers on Cnacting on Sobolev Spaces. (C) 2021 Elsevier Inc. All rights reserved.