Article
| Title: | The factorization of the weighted Hardy space in terms of multilinear Calderón-Zygmund operators (English) |
| Author: | He, Suixin |
| Author: | Tao, Shuangping |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 73 |
| Issue: | 1 |
| Year: | 2023 |
| Pages: | 135-149 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | 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. (English) |
| Keyword: | weighted Hardy space |
| Keyword: | weighted BMO space |
| Keyword: | multilinear Calderón-Zygmund operator |
| Keyword: | weak factorization |
| MSC: | 42B20 |
| MSC: | 42B35 |
| idZBL: | Zbl 07655759 |
| idMR: | MR4541093 |
| DOI: | 10.21136/CMJ.2022.0458-21 |
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| Date available: | 2023-02-03T11:10:00Z |
| Last updated: | 2023-09-13 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/151508 |
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| Reference: | [2] Duong, X. T., Li, J., Wick, B. D., Yang, D.: Factorization for Hardy spaces and characterization for BMO spaces via commutators in the Bessel setting.Indiana Univ. Math. J. 66 (2017), 1081-1106. Zbl 1376.42028, MR 3689327, 10.1512/iumj.2017.66.6115 |
| Reference: | [3] Grafakos, L., Torres, R. H.: Maximal operator and weighted norm inequalities for multilinear singular integrals.Indiana Univ. Math. J. 51 (2002), 1261-1276. Zbl 1033.42010, MR 1947875, 10.1512/iumj.2002.51.2114 |
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| Reference: | [5] Li, J., Wick, B. D.: 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. Zbl 1366.42027, MR 3639532, 10.1016/j.jfa.2017.03.007 |
| Reference: | [6] Li, J., Wick, B. D.: Weak factorizations of the Hardy space $H^{1}(\mathbb{R}^n)$ in terms of multilinear Riesz transforms.Can. Math. Bull. 60 (2017), 571-585. Zbl 1372.42018, MR 3679731, 10.4153/CMB-2017-033-9 |
| Reference: | [7] Muckenhoupt, B.: Weighted norm inequalities for the Hardy maximal function.Trans. Am. Math. Soc. 165 (1972), 207-226. Zbl 0236.26016, MR 0293384, 10.1090/S0002-9947-1972-0293384-6 |
| Reference: | [8] Wang, D. H., Zhou, J., Teng, Z. D.: Characterizations of weighted BMO space and its application.Acta. Math. Sin., Engl. Ser. 37 (2021), 1278-1292. Zbl 1473.42021, MR 4305390, 10.1007/s10114-021-9567-6 |
| Reference: | [9] Wang, D., Zhu, R.: Weak factorizations of the Hardy space in terms of multilinear fractional integral operator.Available at https://arxiv.org/abs/2112.06249v1 (2021), 12 pages. MR 4471559 |
| Reference: | [10] Wang, D., Zhu, R., Shu, L.: 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. MR 4576368 |
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