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The Mihlin Multiplier Theorem on Anisotropic Mixed-Norm Hardy Spaces

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Abstract

Let \(\vec {p}\in (0,1]^n\) and \(H_A^{\vec {p}}({\mathbb {R}}^n)\) be the anisotropic mixed-norm Hardy spaces associated with a dilation matrix A. In this paper, we obtain a Mihlin multiplier theorem on anisotropic Hardy spaces \({H_A^{\vec {p}}({{\mathbb {R}}^n})}\), when \(\vec p\) depends on eccentricities of A and the level of regularity of a multiplier symbol. This extends both the multiplier theorems in classical Hardy spaces and anisotropic Hardy spaces.

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Acknowledgements

The author would like to thank the referees for their careful reading and the valuable comments, which do improve the presentation and the readability of this paper.

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  1. School of Mathematics and Information Science, Guangzhou University, Guangzhou, 510006, People’s Republic of China

    Long Huang

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This work was partially supported by the National Natural Science Foundation of China (Grant No. 12201139) and Guangdong Basic and Applied Basic Research Foundation (Grant No. 2021A1515110905).

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Huang, L. The Mihlin Multiplier Theorem on Anisotropic Mixed-Norm Hardy Spaces. Bull. Malays. Math. Sci. Soc. 46, 129 (2023). https://doi.org/10.1007/s40840-023-01512-3

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