TY - JOUR T1 - Boundedness of Commutators Generated by Campanato-Type Functions and Riesz Transforms Associated with Schrödinger Operators AU - Mo , Huixia AU - Yu , Dongyan AU - Sui , Xin JO - Communications in Mathematical Research VL - 4 SP - 289 EP - 297 PY - 2021 DA - 2021/05 SN - 31 DO - http://doi.org/10.13447/j.1674-5647.2015.04.01 UR - https://global-sci.org/intro/article_detail/cmr/18911.html KW - commutator, Campanato-Type space, Riesz transform, Schrödinger operator. AB -

Let $\mathcal{L} = −∆ + V$ be a Schrödinger operator on $\boldsymbol{R}^n , n > 3$, where $∆$ is the Laplacian on $\boldsymbol{R}^n$ and $V ≠ 0$ is a nonnegative function satisfying the reverse Hölder's inequality. Let $[b, T]$ be the commutator generated by the Campanato-type function $b ∈ Λ^β_{\mathcal{L}}$ and the Riesz transform associated with Schrödinger operator $T = ∇(−∆+V )^{\frac{1}{2}}$. In the paper, we establish the boundedness of $[b, T]$ on Lebesgue spaces and Campanato-type spaces.