Perturbed Dyadic Cubes and Quantitative Estimates for Schrödinger Operators with Potentials in RH^n/2

2026/07/31 by Jun Cao, Cheng Chen, Chaohong Deng +1
Mathematics · #math.AP #math.CA #msc:35J10 #msc:47A55 #msc:47A10 #msc:47G40

paper · pdf

42 pages, 5 figures. All comments are welcome

arxiv created 2026/07/31 · arxiv updated 2026/08/03

Abstract

Let L:=-Δ+V be a Schrödinger operator on the Euclidean space ℝⁿ with potential V in the reverse Hölder class RH^n/2 satisfying some mild assumptions that V neither decays too rapidly nor oscillates violently at infinity. In this paper, the authors construct a new system of dyadic cubes D^V that reflects the intrinsic geometry perturbed by V. Then using the quantitative geometric information of D^V, the authors characterize the L^p operator norm of the Riesz potential L^-α/2 for all α∈ (0,2] and p∈ (1,∞). As applications, some quantitative spectral estimates for L are given.

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