TY - JOUR
T1 - Sobolev spaces adapted to the Schrödinger operator with inverse-square potential
AU - Killip, R.
AU - Miao, C.
AU - Visan, M.
AU - Zhang, J.
AU - Zheng, J.
N1 - Publisher Copyright:
© 2017, Springer-Verlag GmbH Deutschland.
PY - 2018/4/1
Y1 - 2018/4/1
N2 - We study the Lp-theory for the Schrödinger operator La with inverse-square potential a| x| - 2. Our main result describes when Lp-based Sobolev spaces defined in terms of the operator (La)s/2 agree with those defined via (- Δ) s/2. We consider all regularities 0 < s< 2. In order to make the paper self-contained, we also review (with proofs) multiplier theorems, Littlewood–Paley theory, and Hardy-type inequalities associated to the operator La.
AB - We study the Lp-theory for the Schrödinger operator La with inverse-square potential a| x| - 2. Our main result describes when Lp-based Sobolev spaces defined in terms of the operator (La)s/2 agree with those defined via (- Δ) s/2. We consider all regularities 0 < s< 2. In order to make the paper self-contained, we also review (with proofs) multiplier theorems, Littlewood–Paley theory, and Hardy-type inequalities associated to the operator La.
KW - Heat kernel estimate
KW - Inverse-square potential
KW - Littlewood–Paley theory
KW - Mikhlin multiplier theorem
KW - Riesz transforms
UR - https://www.scopus.com/pages/publications/85030691700
U2 - 10.1007/s00209-017-1934-8
DO - 10.1007/s00209-017-1934-8
M3 - Article
AN - SCOPUS:85030691700
SN - 0025-5874
VL - 288
SP - 1273
EP - 1298
JO - Mathematische Zeitschrift
JF - Mathematische Zeitschrift
IS - 3-4
ER -