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Weighted norm inequalities related to fractional Schrödinger operators

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Abstract

Let \(L=-\Delta +V\) be a Schrödinger operator on \(\mathbb {R}^{n}\) with \(n\ge 3\), where the nonnegative potential V satisfies a reverse Hölder inequality. This paper is devoted to investigating the bounded behaviors of the semigroup maximal operators and fractional square functions related to the Schrödinger operator and their corresponding commutators on the weighted Morrey spaces containing many well-known Morrey spaces. In order to achieve these goals, we establish some weighted \(L^{p}\) norm inequalities for the above operators, where the classes of weights associated with the auxiliary function contain the classical Muckenhoupt weights.

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Acknowledgements

P. T. Li was supported by the National Natural Science Foundation of China (No. 12071272); Shandong Natural Science Foundation of China (No. ZR2020MA004). Y. Liu was supported by the National Natural Science Foundation of China (No. 11671031, No. 12271042) and Beijing Natural Science Foundation of China (No. 1232023).

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Authors and Affiliations

  1. School of Mathematics and Physics, University of Science and Technology Beijing, Beijing, 100083, China

    Zhiyong Wang & Yu Liu

  2. School of Mathematics and Statistics, Qingdao University, Qingdao, 266071, China

    Pengtao Li

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  1. Zhiyong Wang
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  2. Pengtao Li
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Correspondence to Yu Liu.

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Wang, Z., Li, P. & Liu, Y. Weighted norm inequalities related to fractional Schrödinger operators. J. Pseudo-Differ. Oper. Appl. 14, 73 (2023). https://doi.org/10.1007/s11868-023-00567-x

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