\(H^ p\)-multipliers on stratified groups
The authors give a criterion for boundedness on the Hardy spaces \(H^ p\) for functions M(\({\mathcal L})\) of the sublaplacian \({\mathcal L}\) on a stratified Lie group, when M is bounded, and M and its dilates M(R\(\lambda)\), \(R>0\), are locally in the Lipschitz-Besov space \(\Lambda\) (s;\(\tau\),\(\infty)\) uniformly with respect to R. The criterion requires that \(r>0\) (not necessarily an integer), \(s>r+(Q/2)+1\) and \(Q(Q+r)<p<\infty\), where Q is the homogeneous dimension of the group. The proof is based on the atomic and molecular characterization of Hardy spaces.
scientific article; zbMATH DE number 4040531
scientific article