WEAK FACTORIZATIONS OF H1(Rn) IN TERMS OF MULTILINEAR FRACTIONAL INTEGRAL OPERATOR ON VARIABLE LEBESGUE SPACES
- Resource Type
- Article
- Authors
- Zongguang Liu; Huan Zhao
- Source
- 대한수학회보, 60(6), pp.1439-1451 Nov, 2023
- Subject
- 수학
- Language
- English
- ISSN
- 2234-3016
1015-8634
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.