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Volume 31, Issue 4
Boundedness of Commutators Generated by Campanato-Type Functions and Riesz Transforms Associated with Schrödinger Operators

Huixia Mo, Dongyan Yu & Xin Sui

DOI: 10.13447/j.1674-5647.2015.04.01

Commun. Math. Res., 31 (2015), pp. 289-297.

Published online: 2021-05

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  • Abstract

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.

  • Keywords

commutator, Campanato-Type space, Riesz transform, Schrödinger operator.

  • AMS Subject Headings

42B20, 42B30, 42B35

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CMR-31-289, author = {Mo , HuixiaYu , Dongyan and Sui , Xin}, title = {Boundedness of Commutators Generated by Campanato-Type Functions and Riesz Transforms Associated with Schrödinger Operators}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {31}, number = {4}, pages = {289--297}, abstract = {

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} }
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.

Mo , HuixiaYu , Dongyan and Sui , Xin. (2021). Boundedness of Commutators Generated by Campanato-Type Functions and Riesz Transforms Associated with Schrödinger Operators. Communications in Mathematical Research . 31 (4). 289-297. doi:10.13447/j.1674-5647.2015.04.01
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