On homogeneous Besov spaces for 1D Hamiltonians without zero resonance

Vladimir Georgiev, Anna Rita Giammetta

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1 Citation (Scopus)

Abstract

We consider the 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 B˙p s(R), p∈(1,∞) and the corresponding perturbed homogeneous Besov spaces associated with the perturbed Hamiltonian H=−∂x 2+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.

Original languageEnglish
Pages (from-to)155-186
Number of pages32
JournalJournal des Mathematiques Pures et Appliquees
Volume110
DOIs
Publication statusPublished - 2018 Feb

Keywords

  • Elliptic estimates
  • Equivalent Besov norms
  • Homogeneous Besov norms
  • Laplace operator with potential
  • Paley Littlewood decomposition

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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