Commun. Math. Res., 31 (2015), pp. 289-297.
Published online: 2021-05
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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.
}, issn = {2707-8523}, doi = {https://doi.org/10.13447/j.1674-5647.2015.04.01}, url = {http://global-sci.org/intro/article_detail/cmr/18911.html} }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.