Sobolev spaces adapted to the Schrödinger operator with inverse-square potential
Killip R, Miao C, Vişan M, Zhang J, Zheng J. 2018. Sobolev spaces adapted to the Schrödinger operator with inverse-square potential. Mathematische Zeitschrift. 288(3–4), 1273–1298.
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Author
Killip, R.;
Miao, C.;
Vişan, MonicaISTA;
Zhang, J.;
Zheng, J.
Abstract
We study the L p-theory for the Schrödinger operatorLa with inverse-square potential
a|x|^−2. Our main result describes when L p-based Sobolev spaces defined in terms of the
operator (La)^s/2 agree with those defined via (−)^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.
Publishing Year
Date Published
2018-04-01
Journal Title
Mathematische Zeitschrift
Publisher
Springer Nature
Volume
288
Issue
3-4
Page
1273-1298
ISSN
eISSN
IST-REx-ID
Cite this
Killip R, Miao C, Vişan M, Zhang J, Zheng J. Sobolev spaces adapted to the Schrödinger operator with inverse-square potential. Mathematische Zeitschrift. 2018;288(3-4):1273-1298. doi:10.1007/s00209-017-1934-8
Killip, R., Miao, C., Vişan, M., Zhang, J., & Zheng, J. (2018). Sobolev spaces adapted to the Schrödinger operator with inverse-square potential. Mathematische Zeitschrift. Springer Nature. https://doi.org/10.1007/s00209-017-1934-8
Killip, R., C. Miao, Monica Vişan, J. Zhang, and J. Zheng. “Sobolev Spaces Adapted to the Schrödinger Operator with Inverse-Square Potential.” Mathematische Zeitschrift. Springer Nature, 2018. https://doi.org/10.1007/s00209-017-1934-8.
R. Killip, C. Miao, M. Vişan, J. Zhang, and J. Zheng, “Sobolev spaces adapted to the Schrödinger operator with inverse-square potential,” Mathematische Zeitschrift, vol. 288, no. 3–4. Springer Nature, pp. 1273–1298, 2018.
Killip R, Miao C, Vişan M, Zhang J, Zheng J. 2018. Sobolev spaces adapted to the Schrödinger operator with inverse-square potential. Mathematische Zeitschrift. 288(3–4), 1273–1298.
Killip, R., et al. “Sobolev Spaces Adapted to the Schrödinger Operator with Inverse-Square Potential.” Mathematische Zeitschrift, vol. 288, no. 3–4, Springer Nature, 2018, pp. 1273–98, doi:10.1007/s00209-017-1934-8.
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