Acta mathematica scientia,Series B ›› 2024, Vol. 44 ›› Issue (1): 386-404.doi: 10.1007/s10473-024-0121-3
Wei Ding1, Yan Tang1, Yueping Zhu2,†
Received:
2022-07-17
Revised:
2023-06-17
Online:
2024-02-25
Published:
2024-02-27
Contact:
† Yueping Zhu, E-mail: zhuyueping@ntu.edu.cn
About author:
Wei Ding, E-mail: dingwei@ntu.edu.cn; Yan Tang, E-mail: 994585863@qq.com
CLC Number:
Wei Ding, Yan Tang, Yueping Zhu. THE BOUNDEDNESS OF OPERATORS ON WEIGHTED MULTI-PARAMETER LOCAL HARDY SPACES*[J].Acta mathematica scientia,Series B, 2024, 44(1): 386-404.
[1] Coifman R R. A real variable characterization of $H_p$. Studia Math, 1974, 51: 269-274 [2] Fefferman C, Stein E M. $H^{p}$ spaces of several variables. Acta Math, 1972, 129: 137-195 [3] Garcia-Cuerva J. Weighted $H^{p}$ spaces. Dissertations Math, 1979, 162: 1-63 [4] Carbery A, Seeger A. $H^p$ and $L^p$-variants of multiparameter Calderón-Zygmund theory. Trans Amer Math Soc, 1992, 334: 719-747 [5] Chang S Y A. Carleson measures on the bi-disc. Ann of Math, 1979, 109: 613-620 [6] Chang S Y A, Fefferman R. A continuous version of duality of $H^1$ with BMO on the bidisc. Ann of Math, 1980, 112: 179-201 [7] Chang S Y A, Fefferman R. The Calderón-Zygmund decomposition on product domains. Amer J Math, 1982, 104: 455-468 [8] Chang S Y A, Fefferman R. Some recent developments in Fourier analysis and $H^p$ theory on product domains. Bull Amer Math Soc, 1985, 12: 1-43 [9] Carleson L. A counterexample for measures bounded on $H^p$ for the bidisc. Mittag-Leffler Report, 1974, No.7 [10] Cordoba A, Fefferman C. A weighted norm inequality for singular integrals. Studia Math, 1976, 57(1): 97-101 [11] Ding W, Lu G. Duality of multi-parameter Triebel-Lizorkin spaces associated with the composition of two singular integral operators. Trans Amer Math Soc, 2016, 368(10): 7119-7152 [12] Ding W, Lu G. Fefferman type criterion on weighted bi-parameter local Hardy spaces and boundedness of bi-parameter pseudodifferential operators. Forum Math, 2022, 34(6): 1679-1705 [13] Ding W, Lu G, Zhu Y. Multi-parameter Triebel-Lizorkin spaces associated with different homogeneities and its atomic decomposition. Forum Math, 2016, 28: 25-42 [14] Ding W, Lu G, Zhu Y. Multi-parameter local Hardy spaces. Nonlinear Analysis, 2019, 184: 352-380 [15] Ding W, Lu G, Zhu Y. Discrete Littlewood-Paley Characterization of multi parameter local hardy spaces. Forum Math, 2019, 31: 1467-1488 [16] Ding W, Zhu Y. Weighted multi-parameter mixed Hardy spaces and their applications. Acta Mathematica Scientia, 2020, 40B(4): 945-969 [17] Ding Y, Han Y, Lu G, Wu X. Boundedness of singular integrals on multiparameter weighted Hardy spaces $H^p_w (R^n\times R^m)$. Potential Anal, 2012, 37: 31-56 [18] Ding Y, Lu G, Ma B. Multi-parameter Triebel-Lizorkin and Besov spaces associated with flag singular integrals. Acta Math Sin Engl Ser, 2010, 26: 603-620 [19] Fefferman R. Calderón-Zygmund theory for product domains-$H^p$ spaces. Proc Nat Acad Sci, 1986, 83: 840-843 [20] Fefferman R. Strong differentiation with respect to measures. Amer J Math, 1981, 103: 33-40 [21] Fefferman R. $A^{p}$ weight and singular integrals. Amer J Math, 1988, 110(5): 975-987 [22] Fefferman R. Harmonic analysis on product spaces. Ann of Math, 1987, 126: 109-130 [23] Fefferman R, Stein E M. Singular integrals on product spaces. Adv Math, 1982, 45: 117-143 [24] Garcia Cuerva J, Rubio de Francia J L. Weighted Norm Inequalities and Related Topics. Amsterdam: North Holland, 1985 [25] Grafakos L.Classical and Modern Fourier Analysis. Englewood Cliffs, NJ: Pearson Prentice Hall, 2008 [26] Gundy R, Stein E M. $H^p$ theory for the polydisk. Proc Nat Acad Sci, 1979, 76: 1026-1029 [27] Han Y, Lu G, Ruan Z. Boundedness criterion of Journé's class of singular integrals on multiparameter Hardy spaces. J Funct Anal, 2013, 264(5): 1238-1268 [28] Han Y, Lu G, Ruan Z. Boundedness of singular Integrals in Journé's class on weighted multiparameter Hardy spaces. J Geom Anal, 2014 24(4): 2186-2228 [29] Han Y, Lu G, Sawyer E. Flag Hardy spaces and Marcinkiewicz multipliers on the Heisenberg group. Anal PDE, 2014, 7: 1465-1534 [30] Han Y, Lu G, Zhao K. Discrete Calderón's identity, atomic Decomposition and boundedness criterion of operators on multiparameter Hardy spaces. J Geom Anal, 2010, 20: 670-689 [31] Hardy G H. The mean value of the modulus of an analytic function. Proc Lond Math Soc, 1915, 14(2): 269-277 [32] He Sh, Chen J. Weighted multi-parameter local Hardy spaces. Rocky Mountain Journal of Mathematics, 2021, 51(5): 1649-1670 [33] Latter R H. A characterization of $H^{p}(\mathbb{R}^{n})$ in terms of atoms. Studia Math, 1978, 62: 93-101 [34] Lu G, Ruan Z. Duality theory of weighted Hardy spaces with arbitrary number of parameters. Forum Math, 2014, 26: 1429-1457 [35] Lu G, Xiao Y. Dual spaces of weighted multi-parameter Hardy spaces associated with the Zygmund dilation. Adv Nonlinear Stud, 2012, 12: 533-553 [36] Lu G, Zhu Y. Singular integrals and weighted Triebel-Lizorkin and Besov spaces of arbitrary number of parameters. Acta Math Sin Engl Ser, 2013, 29: 39-52 [37] Ruan Z. Weighted Hardy spaces in three-parameter case. J Math Anal Appl, 2010, 367(2): 625-639 [38] Pipher J. Journe's covering lemma and its extension to higher dimensions. Duke Math J, 1986, 53: 683-690 [39] Stein E M, Weiss G. On the theory of harmonic functions of several variables. I. The theory of $H_p$-spaces. Acta Math, 1960, 103: 25-62 [40] Yang D, Liang Y,Ky L D.Real-Variable Theory of Musielak-Orlicz Hardy Spaces. Cham: Springer, 2017 [41] Yang D, Yang S. Local Hardy spaces of Musielak-Orlicz type and their applications. Sci China Math, 2012, 55: 1677-1720 [42] Zhu X. Atomic decomposition for weighted $H_{p}$ spaces on product domains. Science in China (Series A), 1992, 35: 158-168 |
[1] | Haiyang Jin, Kaiying Xu. BOUNDEDNESS OF A CHEMOTAXIS-CONVECTION MODEL DESCRIBING TUMOR-INDUCED ANGIOGENESIS* [J]. Acta mathematica scientia,Series B, 2023, 43(1): 156-168. |
[2] | Jie JIANG. BOUNDEDNESS AND EXPONENTIAL STABILIZATION IN A PARABOLIC-ELLIPTIC KELLER–SEGEL MODEL WITH SIGNAL-DEPENDENT MOTILITIES FOR LOCAL SENSING CHEMOTAXIS [J]. Acta mathematica scientia,Series B, 2022, 42(3): 825-846. |
[3] | Shuyan QIU, Chunlai MU, Hong YI. BOUNDEDNESS AND ASYMPTOTIC STABILITY IN A PREDATOR-PREY CHEMOTAXIS SYSTEM WITH INDIRECT PURSUIT-EVASION DYNAMICS [J]. Acta mathematica scientia,Series B, 2022, 42(3): 1035-1057. |
[4] | Jianjun JIN, Shuan TANG. GENERALIZED CESÀRO OPERATORS ON DIRICHLET-TYPE SPACES [J]. Acta mathematica scientia,Series B, 2022, 42(1): 212-220. |
[5] | Naiqi SONG, Heping LIU, Jiman ZHAO. BILINEAR SPECTRAL MULTIPLIERS ON HEISENBERG GROUPS [J]. Acta mathematica scientia,Series B, 2021, 41(3): 968-990. |
[6] | Abdelkrim MOUSSAOUI, Jean VELIN. EXISTENCE AND BOUNDEDNESS OF SOLUTIONS FOR SYSTEMS OF QUASILINEAR ELLIPTIC EQUATIONS [J]. Acta mathematica scientia,Series B, 2021, 41(2): 397-412. |
[7] | Qingquan TANG, Qiao XIN, Chunlai MU. BOUNDEDNESS OF THE HIGHER-DIMENSIONAL QUASILINEAR CHEMOTAXIS SYSTEM WITH GENERALIZED LOGISTIC SOURCE [J]. Acta mathematica scientia,Series B, 2020, 40(3): 713-722. |
[8] | ZHANG Xue-Jun, XI Li-Hua, FAN Hai-Xia, LI Jun-Feng. ATOMIC DECOMPOSITION OF μ-BERGMAN SPACE IN Cn [J]. Acta mathematica scientia,Series B, 2014, 34(3): 779-789. |
[9] | Dai-Ji-Neng, OUYANG Cai-Heng. COMPOSITION OPERATORS BETWEEN BLOCH TYPE SPACES IN THE UNIT BALL [J]. Acta mathematica scientia,Series B, 2014, 34(1): 73-81. |
[10] | REN Yan-Bo, GUO Tie-Xin. WEAK ATOMIC DECOMPOSITIONS OF MARTINGALE HARDY-LORENTZ SPACES AND APPLICATIONS [J]. Acta mathematica scientia,Series B, 2012, 32(3): 1157-1166. |
[11] | LI Peng-Tao, PENG Li-Zhong. Lp BOUNDEDNESS OF COMMUTATOR OPERATOR ASSOCIATED WITH SCHRÖDINGER OPERATORS ON HEISENBERG GROUP [J]. Acta mathematica scientia,Series B, 2012, 32(2): 568-578. |
[12] | WANG Mao-Fa. WEIGHTED COMPOSITION OPERATORS BETWEEN DIRICHLET SPACES [J]. Acta mathematica scientia,Series B, 2011, 31(2): 641-651. |
[13] | ZHANG Min-Zhu. BOUNDEDNESS FROM BELOW OF MULTIPLICATION OPERATORS BETWEEN α-BLOCH SPACES ON THE UNIT BALL [J]. Acta mathematica scientia,Series B, 2010, 30(5): 1619-1630. |
[14] | LI Jun-Feng. COMPOSITION OPERATORS FROM p-BLOCH SPACES TO LITTLE q-BLOCH SPACES |ON THE UNIT BALL OF Cn [J]. Acta mathematica scientia,Series B, 2010, 30(3): 1013-1020. |
[15] | YANG Zhan-YIng, YANG Qi-Xiang. A NOTE ON CONVOLUTION-TYPE CALDERÓN-ZYGMUND OPERATORS [J]. Acta mathematica scientia,Series B, 2009, 29(5): 1341-1350. |
|