TY - JOUR
T1 - On homogeneous Besov spaces for 1D Hamiltonians without zero resonance
AU - Georgiev, Vladimir
AU - Giammetta, Anna Rita
N1 - Funding Information:
Funding: This work was supported by University of Pisa , project no. PRA-2016-41 “Fenomeni singolari in problemi deterministici e stocastici ed applicazioni”, by the Contract FIRB “Dinamiche Dispersive: Analisi di Fourier e Metodi Variazionali”, 2012; INDAM , GNAMPA – Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni and Institute of Mathematics and Informatics, Bulgarian Academy of Sciences and Top Global University Project, Waseda University .
Publisher Copyright:
© 2017 Elsevier Masson SAS
PY - 2018/2
Y1 - 2018/2
N2 - 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.
AB - 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.
KW - Elliptic estimates
KW - Equivalent Besov norms
KW - Homogeneous Besov norms
KW - Laplace operator with potential
KW - Paley Littlewood decomposition
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U2 - 10.1016/j.matpur.2017.07.007
DO - 10.1016/j.matpur.2017.07.007
M3 - Article
AN - SCOPUS:85027284084
SN - 0021-7824
VL - 110
SP - 155
EP - 186
JO - Journal des Mathematiques Pures et Appliquees
JF - Journal des Mathematiques Pures et Appliquees
ER -