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Boundedness for Littlewood-Paley functions on weighted Morrey-type spaces related to certain nonnegative potentials

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Abstract

Let \(L:=-\Delta +V\) be the Schrödinger operator on \({\mathbb {R}}^{n}\) with \(n\ge 3\), where V is a nonnegative potential belonging to certain reverse Hölder class \(RH_{q}({\mathbb {R}}^{n})\) with \(q>n/2\). Applying a new class of weights \(A_{p}^{\rho }\) which is larger than the classical Muckenhoupt’s weights, we obtain the boundedness on weighted Morrey-type spaces for Littlewood-Paley functions and their commutators related to L.

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Acknowledgements

J. Zhou was supported by the National Natural Science Foundation of China (Grant No. 11661075). Y. Liu was supported by the National Natural Science Foundation of China (Grant No. 12271042) and Beijing Natural Science Foundation of China (Grant No. 1232023).

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Authors and Affiliations

  1. School of Mathematics and Physics, University of Science and Technology Beijing, Beijing, 100083, People’s Republic of China

    Nan Zhao & Yu Liu

  2. College of Mathematics and System Sciences, Xinjiang University, Urumqi, 830046, People’s Republic of China

    Jiang Zhou

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  1. Nan Zhao
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  2. Jiang Zhou
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Correspondence to Yu Liu.

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Zhao, N., Zhou, J. & Liu, Y. Boundedness for Littlewood-Paley functions on weighted Morrey-type spaces related to certain nonnegative potentials. J. Pseudo-Differ. Oper. Appl. 14, 45 (2023). https://doi.org/10.1007/s11868-023-00538-2

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  • DOI: https://doi.org/10.1007/s11868-023-00538-2

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