The Boundedness of the Commutator for Riesz Potential Associated with Schrödinger Operator on Morrey Spaces

The Boundedness of the Commutator for Riesz Potential Associated with Schrödinger Operator on Morrey Spaces

Year:    2014

Author:    Dongxiang Chen, Liang Song

Analysis in Theory and Applications, Vol. 30 (2014), Iss. 4 : pp. 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 $M_{\alpha,v}^{p_1,q_1}$.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/ata.2014.v30.n4.3

Analysis in Theory and Applications, Vol. 30 (2014), Iss. 4 : pp. 363–368

Published online:    2014-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    6

Keywords:    Reverse Hölder class commutator Schrödinger operator.

Author Details

Dongxiang Chen

Liang Song