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Bull. Korean Math. Soc. 2023; 60(6): 1439-1451

Online first article November 17, 2023      Printed November 30, 2023

https://doi.org/10.4134/BKMS.b220496

Copyright © The Korean Mathematical Society.

Weak factorizations of $H^1(\mathbb{R}^n)$ in terms of multilinear fractional integral operator on variable Lebesgue spaces

Zongguang Liu, Huan Zhao

China University of Mining and Technology; Zhejiang University of Science and Technology

Abstract

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This paper provides a constructive proof of the weak factorizations of the classical Hardy space $H^1(\mathbb{R}^n)$ in terms of multilinear fractional integral operator on the variable Lebesgue spaces, which the result is new even in the linear case. As a direct application, we obtain a new proof of the characterization of $\mathrm{BMO}(\mathbb{R}^n)$ via the boundedness of commutators of the multilinear fractional integral operator on the variable Lebesgue spaces.

Keywords: Hardy space, $\mathrm{BMO}$ space, multilinear fractional integral operator, weak factorization

MSC numbers: 42B35, 42B20

Supported by: Supported by the National Natural Science Foundation of China (No.11671397).

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