Czechoslovak Mathematical Journal, Vol. 73, No. 1, pp. 135-149, 2023
The factorization of the weighted Hardy space in terms of multilinear Calderón-Zygmund operators
Suixin He, Shuangping Tao
Received December 10, 2021. Published online July 30, 2022.
Abstract: We give a constructive proof of the factorization theorem for the weighted Hardy space in terms of multilinear Calderón-Zygmund operators. The result is also new even in the linear setting. As an application, we obtain the characterization of weighted BMO space via the weighted boundedness of commutators of the multilinear Calderón-Zygmund operators.
References: [1] R. R. Coifman, R. Rochberg, G. Weiss: Factorization theorems for Hardy spaces in several variables. Ann. Math. (2) 103 (1976), 611-635. DOI 10.2307/1970954 | MR 0412721 | Zbl 0326.32011
[2] X. T. Duong, J. Li, B. D. Wick, D. Yang: Factorization for Hardy spaces and characterization for BMO spaces via commutators in the Bessel setting. Indiana Univ. Math. J. 66 (2017), 1081-1106. DOI 10.1512/iumj.2017.66.6115 | MR 3689327 | Zbl 1376.42028
[3] L. Grafakos, R. H. Torres: Maximal operator and weighted norm inequalities for multilinear singular integrals. Indiana Univ. Math. J. 51 (2002), 1261-1276. DOI 10.1512/iumj.2002.51.2114 | MR 1947875 | Zbl 1033.42010
[4] A. K. Lerner, S. Ombrosi, C. Pérez, R. H. Torres, R. Trujillo-González: New maximal functions and multiple weights for the multilinear Calderón-Zygmund theory. Adv. Math. 220 (2009), 1222-1264. DOI 10.1016/j.aim.2008.10.014 | MR 2483720 | Zbl 1160.42009
[5] J. Li, B. D. Wick: Characterizations of $H^1_{\Delta_N}(\mathbb{R}^n)$ and BMO$_{\Delta_N}(\mathbb{R}^n)$ via weak factorizations and commutators. J. Funct. Anal. 272 (2017), 5384-5416. DOI 10.1016/j.jfa.2017.03.007 | MR 3639532 | Zbl 1366.42027
[6] J. Li, B. D. Wick: Weak factorizations of the Hardy space $H^1(\mathbb{R}^n)$ in terms of multilinear Riesz transforms. Can. Math. Bull. 60 (2017), 571-585. DOI 10.4153/CMB-2017-033-9 | MR 3679731 | Zbl 1372.42018
[7] B. Muckenhoupt: Weighted norm inequalities for the Hardy maximal function. Trans. Am. Math. Soc. 165 (1972), 207-226. DOI 10.1090/S0002-9947-1972-0293384-6 | MR 0293384 | Zbl 0236.26016
[8] D. H. Wang, J. Zhou, Z. D. Teng: Characterizations of weighted BMO space and its application. Acta. Math. Sin., Engl. Ser. 37 (2021), 1278-1292. DOI 10.1007/s10114-021-9567-6 | MR 4305390 | Zbl 1473.42021
[9] D. Wang, R. Zhu: Weak factorizations of the Hardy space in terms of multilinear fractional integral operator. Available at https://arxiv.org/abs/2112.06249v1 (2021), 12 pages.
[10] D. Wang, R. Zhu, L. Shu: The factorizations of $H^\rho(\mathbb{R}^n)$ via multilinear Calderón-Zygmund operators on weighted Lebesgue spaces. Available at https://arxiv.org/abs/2112.06252v1 (2021), 22 pages.
Affiliations: Suixin He, Shuangping Tao (corresponding author), College of Mathematics and Statistics, Northwest Normal University, Lanzhou, Gansu, 730070, P. R. China, e-mail: hesuixinmath@126.com, taosp@nwnu.edu.cn
