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Title: Weighted multi-parameter mixed Hardy spaces and their applications (English)
Author: Ding, Wei
Author: Xu, Yun
Author: Zhu, Yueping
Language: English
Journal: Czechoslovak Mathematical Journal
ISSN: 0011-4642 (print)
ISSN: 1572-9141 (online)
Volume: 72
Issue: 3
Year: 2022
Pages: 709-734
Summary lang: English
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Category: math
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Summary: Applying discrete Calderón's identity, we study weighted multi-parameter mixed Hardy space $H^{p}_{\rm mix}(\omega ,\mathbb {R}^{n_{1}}\times \mathbb {R}^{n_{2}})$. Different from classical multi-parameter Hardy space, this space has characteristics of local Hardy space and Hardy space in different directions, respectively. As applications, we discuss the boundedness on $H^{p}_{\rm mix}(\omega ,\mathbb {R}^{n_{1}}\times \mathbb {R}^{n_{2}})$ of operators in mixed Journé's class. (English)
Keyword: weight
Keyword: multi-parameter
Keyword: mixed Hardy spaces
Keyword: singular integral operator
MSC: 42B20
MSC: 42B25
MSC: 42B30
MSC: 42B35
idZBL: Zbl 07584097
idMR: MR4467937
DOI: 10.21136/CMJ.2022.0115-21
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Date available: 2022-08-22T08:18:30Z
Last updated: 2024-10-04
Stable URL: http://hdl.handle.net/10338.dmlcz/150612
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Reference: [1] Coifman, R. R.: A real variable characterization of $H^p$.Stud. Math. 51 (1974), 269-274. Zbl 0289.46037, MR 0358318, 10.4064/sm-51-3-269-274
Reference: [2] Coifman, R. R., Weiss, G.: Extensions of Hardy spaces and their use in analysis.Bull. Am. Math. Soc. 83 (1977), 569-645. Zbl 0358.30023, MR 0447954, 10.1090/S0002-9904-1977-14325-5
Reference: [3] Cruz-Uribe, D., Martell, J. M., Pérez, C.: Sharp weighted estimates for classical operators.Adv. Math. 229 (2012), 408-441. Zbl 1236.42010, MR 2854179, 10.1016/j.aim.2011.08.013
Reference: [4] Ding, Y., Han, Y., Lu, G., Wu, X.: Boundedness of singular integrals on multiparameter weighted Hardy spaces $H^p_w({\mathbb R}^n\times {\mathbb R}^m)$.Potential Anal. 37 (2012), 31-56. Zbl 1271.42017, MR 2928237, 10.1007/s11118-011-9244-y
Reference: [5] Ding, W., Lu, G., Zhu, Y.: Multi-parameter local Hardy spaces.Nonlinear Anal., Theory Methods Appl., Ser. A 184 (2019), 352-380. Zbl 1418.42038, MR 3925053, 10.1016/j.na.2019.02.014
Reference: [6] Ding, W., Qin, M., Zhu, Y.: The boundedness on mixed Hardy spaces.J. Funct. Spaces 2020 (2020), Article ID 5341674, 12 pages. Zbl 1436.42018, MR 4078744, 10.1155/2020/5341674
Reference: [7] Ding, W., Zhu, Y.: Mixed Hardy spaces and their applications.Acta Math. Sci., Ser. B, Engl. Ed. 40 (2020), 945-969. MR 4108498, 10.1007/s10473-020-0405-1
Reference: [8] Fefferman, C. L., Stein, E. M.: $H^p$ spaces of several variables.Acta Math. 129 (1972), 137-193. Zbl 0257.46078, MR 0447953, 10.1007/BF02392215
Reference: [9] Fefferman, R.: Strong differentiation with respect to measures.Am. J. Math. 103 (1981), 33-40. Zbl 0475.42019, MR 0601461, 10.2307/2374188
Reference: [10] Fefferman, R.: The atomic decomposition of $H^1$ in product spaces.Adv. Math. 55 (1985), 90-100. Zbl 0606.42016, MR 0772072, 10.1016/0001-8708(85)90006-4
Reference: [11] Fefferman, R.: Calderón-Zygmund theory for product domains: $H^p$ spaces.Proc. Natl. Acad. Sci. USA 83 (1986), 840-843. Zbl 0602.42023, MR 0828217, 10.1073/pnas.83.4.840
Reference: [12] Fefferman, R.: Harmonic analysis on product spaces.Ann. Math. (2) 126 (1987), 109-130. Zbl 0644.42017, MR 0898053, 10.2307/1971346
Reference: [13] Fefferman, R., Stein, E. M.: Singular integrals on product spaces.Adv. Math. 45 (1982), 117-143. Zbl 0517.42024, MR 0664621, 10.1016/S0001-8708(82)80001-7
Reference: [14] Folland, G. B., Stein, E. M.: Hardy Spaces on Homogeneous Groups.Mathematical Notes 28. Princeton University Press, Princeton (1982). Zbl 0508.42025, MR 0657581, 10.2307/j.ctv17db3q0
Reference: [15] Garcia-Cuerva, J.: Weighted $H^p$ spaces.Diss. Math. 162 (1979), 63 pages. Zbl 0434.42023, MR 0549091
Reference: [16] Garcia-Cuerva, J., Francia, J. L. Rubio de: Weighted Norm Inequalities and Related Topics.North-Holland Mathematics Studies 116. North-Holland, Amsterdam (1985). Zbl 0578.46046, MR 0807149, 10.1016/s0304-0208(08)x7154-3
Reference: [17] Goldberg, D.: A local version of real Hardy spaces.Duke Math. J. 46 (1979), 27-42. Zbl 0409.46060, MR 0523600, 10.1215/S0012-7094-79-04603-9
Reference: [18] Grafakos, L.: Classical and Modern Fourier Analysis.Pearson/Prentice Hall, Upper Saddle River (2004). Zbl 1148.42001, MR 2449250
Reference: [19] Gundy, R. F., Stein, E. M.: $H^p$ theory for the poly-disk.Proc. Natl. Acad. Sci. USA 76 (1979), 1026-1029. Zbl 0405.32002, MR 0524328, 10.1073/pnas.76.3.1026
Reference: [20] Gundy, R. F., Wheeden, R. L.: Weighted integral inequalities for the nontangential maximal function, Lusin area integral, and Walsh-Paley series.Stud. Math. 49 (1974), 107-124. Zbl 0271.28002, MR 0352854, 10.4064/sm-49-2-107-124
Reference: [21] Han, Y., Lee, M.-Y., Lin, C.-C., Lin, Y.-C.: Calderón-Zygmund operators on product Hardy spaces.J. Funct. Anal. 258 (2010), 2834-2861. Zbl 1197.42006, MR 2593346, 10.1016/j.jfa.2009.10.022
Reference: [22] Han, Y., Lin, C., Lu, G., Ruan, Z., Sawyer, E. T.: Hardy spaces associated with different homogeneities and boundedness of composition operators.Rev. Mat. Iberoam. 29 (2013), 1127-1157. Zbl 1291.42018, MR 3148598, 10.4171/RMI/751
Reference: [23] Han, Y., Lu, G., Ruan, Z.: Boundedness criterion of Journé's class of singular integrals on multiparameter Hardy spaces.J. Funct. Anal. 264 (2013), 1238-1268. Zbl 1268.42024, MR 3010020, 10.1016/j.jfa.2012.12.006
Reference: [24] Han, Y., Lu, G., Ruan, Z.: Boundedness of singular integrals in Journé's class on weighted multiparameter Hardy spaces.J. Geom. Anal. 24 (2014), 2186-2228. Zbl 1302.42024, MR 3261735, 10.1007/s12220-013-9421-x
Reference: [25] Han, Y., Lu, G., Zhao, K.: Discrete Calderón's identity, atomic decomposition and boundedness criterion of operators on multiparameter Hardy spaces.J. Geom. Anal. 20 (2010), 670-689. Zbl 1193.42090, MR 2610894, 10.1007/s12220-010-9123-6
Reference: [26] Hardy, G. H.: The mean value of the modulus of an analytic function.Proc. Lond. Math. Soc. (2) 14 (1915), 269-277 \99999JFM99999 45.1331.03. 10.1112/plms/s2_14.1.269
Reference: [27] Journé, J.-L.: Calderón-Zygmund operators on product spaces.Rev. Mat. Iberoam. 1 (1985), 55-91. Zbl 0634.42015, MR 0836284, 10.4171/RMI/15
Reference: [28] Journé, J.-L.: Two problems of Calderón-Zygmund theory on product-spaces.Ann. Inst. Fourier 38 (1988), 111-132. Zbl 0638.47026, MR 0949001, 10.5802/aif.1125
Reference: [29] Latter, R. H.: A characterization of $H^p(\mathbb{R}^n)$ in terms of atoms.Stud. Math. 62 (1978), 93-101. Zbl 0398.42017, MR 0482111, 10.4064/sm-62-1-93-101
Reference: [30] Lu, G., Zhu, Y.: Singular integrals and weighted Triebel-Lizorkin and Besov spaces of arbitrary number of parameters.Acta Math. Sin., Engl. Ser. 29 (2013), 39-52. Zbl 1261.42030, MR 3001008, 10.1007/s10114-012-1402-7
Reference: [31] Ruan, Z.: Weighted Hardy spaces in three-parameter case.J. Math. Anal. Appl. 367 (2010), 625-639. Zbl 1198.42015, MR 2607286, 10.1016/j.jmaa.2010.02.010
Reference: [32] Stein, E. M., Weiss, G.: On the theory of harmonic functions of several variables. I. The theory of $H^p$-spaces.Acta Math. 103 (1960), 25-62. Zbl 0097.28501, MR 0121579, 10.1007/BF02546524
Reference: [33] Yang, D., Liang, Y., Ky, L. D.: Real-Variable Theory of Musielak-Orlicz Hardy Spaces.Lecture Notes in Mathematics 2182. Springer, Cham (2017). Zbl 1375.42038, MR 3586020, 10.1007/978-3-319-54361-1
Reference: [34] Yang, D., Yang, S.: Local Hardy spaces of Musielak-Orlicz type and their applications.Sci. China, Math. 55 (2012), 1677-1720. Zbl 1266.42055, MR 2955251, 10.1007/s11425-012-4377-z
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