[1] Bui T, Ly F. Calderón-Zygmund operators on local Hardy spaces. Potential Anal, 2024, $\textbf{60}$(1): 533-551
[2] Chang S-Y A, Fefferman R. A continuous version of duality of $H^1$ with BMO on the bidisc. Ann Math, 1980, $\textbf{112}$(1): 179-201
[3] Chang S-Y A, Fefferman R. The Calderón-Zygmund decomposition on product domains. Amer J Math, 1982, $\textbf{104}$(3): 455-468
[4] Chang S-Y A, Fefferman R. Some recent developments in Fourier analysis and $H^p$ theory on product domains. Bull Amer Math Soc, 1985, $\textbf{12}$(1): 1-43
[5] Cheeger J. Differentiability of Lipschitz functions on metric measure spaces. Geom Funct Anal, 1999, $\textbf{9}$(3): 428-517
[6] Ding W, Lu G. Boundedness of inhomogeneous Journé's type operators on multi-parameter local Hardy spaces. Nonlinear Analysis, 2020, $\textbf{197}$: 111816
[7] Ding W, Lu G, Zhu Y. Discrete Littlewood-Paley-Stein characterization of multi-parameter local Hardy spaces. Forum Math, 2019, $\textbf{31}$(6): 1467-1488
[8] Fefferman C, Stein E M. $H^p$ spaces of several variables. Acta Math, 1972, $\textbf{129}$(3/4): 137-193
[9] Fefferman R. Singular integrals on product $H^p$ spaces. Rev Mat Iberoam, 1985, $\textbf{1}$(2): 25-31
[10] Fefferman R. Calderón-Zygmund theory for product domains: $H^p$ spaces. Proc Nat Acad Sci, 1986, $\textbf{83}$(4): 840-843
[11] Fefferman R. Harmonic analysis on product spaces. Ann Math, 1987, $\textbf{126}$(1): 109-130
[12] Fefferman R, Pipher J. Multiparameter operators and sharp weighted inequalities. Amer J Math, 1997, $\textbf{119}$(2): 337-369
[13] Fefferman R, Stein E M. Singular integrals on product spaces. Adv Math, 1982, $\textbf{45}$(2): 117-143
[14] Goldberg D. A local version of real Hardy spaces. Duke Math J, 1979, $\textbf{46}$(1): 27-42
[15] Gundy R, Stein E M. $H^p$ theory for the poly-disk. Proc Nat Acad Sci, 1979, $\textbf{76}$(3): 1026-1029
[16] Han Y, Han Y. Boundedness of composition operators associated with mixed homogeneities on Lipschitz spaces. Math Res Lett, 2016, $\textbf{23}$(5): 1387-1403
[17] Han Y, Han Y, Li J, et al. Marcinkiewicz multipliers and Lipschitz spaces on Heisenberg groups. Canad J Math, 2019, $\textbf{71}$(3): 607-627
[18] Han Y, Lee M, Lin C, et al. Calderón-Zygmund operators on product Hardy spaces. J Funct Anal, 2010, $\textbf{258}$(8): 2834-2861
[19] Han Y, Lu G, Sawyer E. Flag Hardy space and Marcinkiewicz multipliers on the Heisnberg group. Anal PDE, 2014, $\textbf{7}$(7): 1465-1534
[20] Harboure E, Salinas O, Viviani B. Boundedness of the fractional integral on weighted Lebesgue and Lipschitz spaces. Trans Amer Math Soc, 1997, $\textbf{349}$(1): 235-255
[21] He S, Chen J. Three-parameter Hardy spaces associated with a sum of two flag singular integrals. Banach J Math Anal, 2020, $\textbf{14}$(4): 1363-1386
[22] He S, Chen J. Boundedness of multi-parameter pseudo-differential operators on multi-parameter Lipschitz spaces. J Pseudo-Differ Oper Appl, 2020, $\textbf{11}$(4): 1665-1683
[23] He S, Chen J. Weighted multiparameter local Hardy spaces. Rocky Mountain J Math, 2021, $\textbf{51}$(5): 1649-1670
[24] He S, Chen J. Inhomogeneous Lipschitz spaces associated with flag singular integrals and their applications. Math Inequal Appl, 2021, $\textbf{24}$(4): 965-987
[25] He S, Chen J. Mixed Lipschitz spaces and their applications. Acta Mathematica Scientia, 2022, $\textbf{42B}$(2): 690-714
[26] He S, Chen J. Duality of three-parameter Hardy spaces associated with a sum of two flag singular integrals. Front Math, 2023, $\textbf{18}$(4): 837-862
[27] He S, Chen J. Characterizations of local product kernels and Hardy spaces. New York J Math, 2025, $\textbf{31}$: 66-90
[28] He S, Zheng T. Boundedness of Calderón-Zygmund operators on inhomogeneous product Lipschitz spaces. J Korean Math Soc, 2022, $\textbf{59}$(3): 469-494
[29] Journé J L. Calderón-Zygmund operators on product spaces. Rev Mat Iberoam, 1985, $\textbf{1}$(3): 55-91
[30] Müller D, Ricci F, Stein E M. Marcinkiewicz multipliers and multi-parameter strucure on Heisenberg(-type) groups I. Invent Math, 1995, $\textbf{119}$(2): 119-233
[31] Müller D, Ricci F, Stein E M. Marcinkiewicz multipliers and multi-parameter strucure on Heisenberg(-type) groups II. Math Z, 1996, $\textbf{221}$(2): 267-291
[32] Nagel A, Ricci F, Stein E M. Singular integrals with flag kernel and analysis on quadratic CR manifolds. J Func Anal, 2001, $\textbf{181}$(1): 29-118
[33] Nagel A, Ricci F, Stein E M. Singular integrals with flag kernel on homogeneous group, I. Rev Mat Iberoam, 2012, $\textbf{28}$(3): 673-722
[34] Nagel A, Ricci F, Stein E M, et al.Algebrals of Singular Integrals Operator with Kernels Controlled by Multiple Norms. Providence, RI: AMS, 2018
[35] Pipher J. Journé's covering lemma and its extension to higher dimensions. Duke Math J, 1986, $\textbf{53}$(3): 683-690
[36] Stein E M, Weiss G. On the theory of harmonic functions of several variables. I. The theory of $H^p$-spaces. Acta Math, 1960, $\textbf{103}$: 25-62
[37] Tan C. Boundedness of classical Calderön-Zygmund convolution operators on product Hardy space. Math Res Lett, 2013, $\textbf{20}$(3): 591-599
[38] Torres R.Boundedness Results for Operators with Singular Kernels on Distribution Spaces. Providence, RI: AMS, 1991
[39] Zheng T, Chen J, Dai J, et al. Calderón-Zygmund operators on homogeneous product Lipschitz spaces.2021, $\textbf{31}$(2): 2033-2057
