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Quantitative weighted estimates for the multilinear pseudo-differential operators in function spaces

  • Jiawei Tan and Qingying Xue EMAIL logo
Published/Copyright: August 6, 2024

Abstract

In this paper, the weighted estimates for multilinear pseudo-differential operators were systematically studied in rearrangement invariant Banach and quasi-Banach spaces. These spaces contain the Lebesgue space, the classical Lorentz space and Marcinkiewicz space as typical examples. More precisely, the weighted boundedness and weighted modular estimates, including the weak endpoint case, were established for multilinear pseudo-differential operators and their commutators. As applications, we show that the above results also hold for the multilinear Fourier multipliers, multilinear square functions, and a class of multilinear Calderón–Zygmund operators.

MSC 2020: 42B20; 42B35

Award Identifier / Grant number: 2020YFA0712900

Award Identifier / Grant number: 12271041

Funding statement: The authors were partly supported by the National Key R&D Program of China (No. 2020YFA0712900) and NNSF of China (No. 12271041).

Acknowledgements

The authors want to express their sincere thanks to the referee for his or her valuable remarks and suggestions, which improve the exposition of the paper.

  1. Communicated by: Christopher D. Sogge

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Received: 2023-12-12
Revised: 2024-06-11
Published Online: 2024-08-06
Published in Print: 2025-06-01

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