Cwikel–Lieb–Rozenblum type inequalities for Hardy–Schrödinger operator

Creators: Duong, Giao Ky; Frank, Rupert L.¹; Le, Thi Minh Thao; Nam, Phan Thành; Nguyen, Phuoc-Tai

1. California Institute of Technology

Abstract

We prove a Cwikel–Lieb–Rozenblum type inequality for the number of negative eigenvalues of the Hardy–Schrödinger operator

on

. The bound is given in terms of a weighted

-norm of W which is sharp in both large and small coupling regimes. We also obtain a similar bound for the fractional Laplacian.

Copyright and License

© 2024 The Author(s). Published by Elsevier Masson SAS. This is an open access
article under the CC BY license (http://creativecommons.org/licenses/by/4.0/)

Acknowledgement

We thank the referees for helpful suggestions. Partial support through the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) Germany's Excellence Strategy EXC - 2111 - 390814868 and through TRR 352 – Project-ID 470903074 (G.K. Duong, R.L. Frank, P.T. Nam), through the U.S. National Science Foundation grant DMS-1954995 (R.L. Frank), and through the Czech Science Foundation Project GA22-17403S (T.M.T. Le, P.T. Nam, P.T. Nguyen) is acknowledged.

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