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Hardy factorization in terms of fractional commutators in Lorentz spaces

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Abstract

We provide a constructive proof of H1 (ℝd) (the classical Hardy space) factorization in terms of fractional commutators in Lorentz spaces. As a direct application, we obtain a characterization of functions in BMO space. Furthermore, we also obtain a Lorentz compactness characterization of fractional commutators.

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Acknowledgements

The author would like to thank the referees for their valuable comments which were very helpful for improving the manuscript. This research was funded by University of Economics Ho Chi Minh City, Vietnam.

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  1. Institute of Applied Mathematics, University of Economics Ho Chi Minh City, Ho Chi Minh City, Vietnam

    Nguyen Anh Dao

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  1. Nguyen Anh Dao
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Correspondence to Nguyen Anh Dao.

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Dao, N.A. Hardy factorization in terms of fractional commutators in Lorentz spaces. Front. Math 17, 853–873 (2022). https://doi.org/10.1007/s11464-021-0946-1

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  • DOI: https://doi.org/10.1007/s11464-021-0946-1

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