Sobolev spaces adapted to the Schrödinger operator with inverse-square potential

article Sobolev spaces adapted to the Schrödinger operator with inverse-square potential published yes R. Killip author C. Miao author Monica Visan author 056daca0-b8d1-11f0-964f-f91054abf8ca J. Zhang author J. Zheng author 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. Springer Nature2018 eng Mathematische Zeitschrift 0025-5874 1432-1823 1503.0271610.1007/s00209-017-1934-8 2883-41273-1298 yes R. Killip, C. Miao, M. Vişan, J. Zhang, J. Zheng, Mathematische Zeitschrift 288 (2018) 1273–1298. 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:<a href="https://doi.org/10.1007/s00209-017-1934-8">10.1007/s00209-017-1934-8</a> 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., 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. <a href="https://doi.org/10.1007/s00209-017-1934-8">https://doi.org/10.1007/s00209-017-1934-8</a>. 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:<a href="https://doi.org/10.1007/s00209-017-1934-8">10.1007/s00209-017-1934-8</a>. 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. <a href="https://doi.org/10.1007/s00209-017-1934-8">https://doi.org/10.1007/s00209-017-1934-8</a> 220422026-06-19T07:46:14Z2026-06-25T07:36:26Z