arrow
Volume 30, Issue 4
The Boundedness of the Commutator for Riesz Potential Associated with Schrödinger Operator on Morrey Spaces

Dongxiang Chen & Liang Song

Anal. Theory Appl., 30 (2014), pp. 363-368.

Published online: 2014-11

Export citation
  • Abstract

Let $\mathcal{L}=-\Delta+V$ be the Schrödinger operator on $\mathbb{R}^d$, where $\Delta$ is the Laplacian on $\mathbb{R}^{d}$ and $V\ne0$ is a nonnegative function satisfying the reverse Hölder's inequality. The authors prove that Riesz potential $\mathcal{J}_{\beta}$ and its commutator $[b,\mathcal{J}_{\beta}]$ associated with $\mathcal{L}$ map from $M_{\alpha,v}^{p,q}$ into $M_{\alpha,v}^{p_1,q_1}$.

  • AMS Subject Headings

42B25, 42B35, 26D15

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{ATA-30-363, author = {Dongxiang Chen , and Liang Song , }, title = {The Boundedness of the Commutator for Riesz Potential Associated with Schrödinger Operator on Morrey Spaces}, journal = {Analysis in Theory and Applications}, year = {2014}, volume = {30}, number = {4}, pages = {363--368}, abstract = {

Let $\mathcal{L}=-\Delta+V$ be the Schrödinger operator on $\mathbb{R}^d$, where $\Delta$ is the Laplacian on $\mathbb{R}^{d}$ and $V\ne0$ is a nonnegative function satisfying the reverse Hölder's inequality. The authors prove that Riesz potential $\mathcal{J}_{\beta}$ and its commutator $[b,\mathcal{J}_{\beta}]$ associated with $\mathcal{L}$ map from $M_{\alpha,v}^{p,q}$ into $M_{\alpha,v}^{p_1,q_1}$.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.2014.v30.n4.3}, url = {http://global-sci.org/intro/article_detail/ata/4500.html} }
TY - JOUR T1 - The Boundedness of the Commutator for Riesz Potential Associated with Schrödinger Operator on Morrey Spaces AU - Dongxiang Chen , AU - Liang Song , JO - Analysis in Theory and Applications VL - 4 SP - 363 EP - 368 PY - 2014 DA - 2014/11 SN - 30 DO - http://doi.org/10.4208/ata.2014.v30.n4.3 UR - https://global-sci.org/intro/article_detail/ata/4500.html KW - Reverse Hölder class, commutator, Schrödinger operator. AB -

Let $\mathcal{L}=-\Delta+V$ be the Schrödinger operator on $\mathbb{R}^d$, where $\Delta$ is the Laplacian on $\mathbb{R}^{d}$ and $V\ne0$ is a nonnegative function satisfying the reverse Hölder's inequality. The authors prove that Riesz potential $\mathcal{J}_{\beta}$ and its commutator $[b,\mathcal{J}_{\beta}]$ associated with $\mathcal{L}$ map from $M_{\alpha,v}^{p,q}$ into $M_{\alpha,v}^{p_1,q_1}$.

Dongxiang Chen , and Liang Song , . (2014). The Boundedness of the Commutator for Riesz Potential Associated with Schrödinger Operator on Morrey Spaces. Analysis in Theory and Applications. 30 (4). 363-368. doi:10.4208/ata.2014.v30.n4.3
Copy to clipboard
The citation has been copied to your clipboard