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Maximal Operator for the Higher Order Calderón Commutator

Part of: Integral, integro-differential, and pseudodifferential operators Normed linear spaces and Banach spaces; Banach lattices Harmonic analysis in several variables

Published online by Cambridge University Press:  03 September 2019

Xudong Lai
Xudong Lai*
Affiliation:
Institute for Advanced Study in Mathematics, Harbin Institute of Technology, Harbin, 150001, People’s Republic of China Email: xudonglai@hit.edu.cnxudonglai@mail.bnu.edu.cn
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Abstract

In this paper, we investigate the weighted multilinear boundedness properties of the maximal higher order Calderón commutator for the dimensions larger than two. We establish all weighted multilinear estimates on the product of the $L^{p}(\mathbb{R}^{d},w)$ space, including some peculiar endpoint estimates of the higher dimensional Calderón commutator.

Keywords

MultilinearCalderón commutatormaximal operatorweighted space

MSC classification

Primary: 42B20: Singular and oscillatory integrals (Calderón-Zygmund, etc.)
Secondary: 42B25: Maximal functions, Littlewood-Paley theory 46B70: Interpolation between normed linear spaces 47G30: Pseudodifferential operators
Type
Article
Information
Canadian Journal of Mathematics , Volume 72 , Issue 5 , October 2020 , pp. 1386 - 1422
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Copyright
© Canadian Mathematical Society 2019

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Footnotes

This work was supported by National Natural Science Foundation of China (No. 11801118), China Postdoctoral Science Foundation (No. 2017M621253, No. 2018T110279), and Fundamental Research Funds for the Central Universities.

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