On homogeneous Besov spaces for 1D Hamiltonians without zero resonance

الأصل · EN

We consider 1-D Laplace operator with short range potential V(x), such that (1+|x|)γV(x) ∈ L¹(R), γ> 1. We study the equivalence of classical homogeneous Besov type spaces Bˢₚ(R), p ∈ (1,∞) and the corresponding perturbed homogeneous Besov spaces associated with the perturbed Hamiltonian H= -∂ₓ² + V(x) on the real line. It is shown that the assumptions 1/p < γ-1 and zero is not a resonance guarantee that the perturbed and unperturbed homogeneous Besov norms of order s ∈ [0,1/p) are equivalent. As a corollary, the corresponding wave operators leave classical homogeneous Besov spaces of order s ∈ [0,1/p) invariant.