Acta mathematica scientia,Series B ›› 2017, Vol. 37 ›› Issue (4): 1083-1104.doi: 10.1016/S0252-9602(17)30059-0
• Articles • Previous Articles Next Articles
Wei DING1, Yueping ZHU2
Received:
2016-01-28
Revised:
2016-09-10
Online:
2017-08-25
Published:
2017-08-25
Contact:
Yueping ZHU,E-mail:zhuyueping@ntu.edu.cn
E-mail:zhuyueping@ntu.edu.cn
About author:
Wei DING,E-mail:dingwei@ntu.edu.cn
Supported by:
Supported by NNSF of China grants (11501308, 11271209, 11371370) and Jiangsu Government Scholarship for Overseas Studies.
Wei DING, Yueping ZHU. DUALITY OF WEIGHTED MULTIPARAMETER TRIEBEL-LIZORKIN SPACES[J].Acta mathematica scientia,Series B, 2017, 37(4): 1083-1104.
[1] Bownik M. Duality and interpolation of anisotropic Triebel-Lizorkin spaces. Math Z, 2008, 259:131-169 [2] Carleson L. A counterexample for measures bounded on Hp for the bidisc. Mittag-Leffler Report, No. 7, 1974 [3] Chang S-Y A, Fefferman R. A continuous version of duality of H1 with BMO on the bidisc. Ann Math, 1980, 112:179-201 [4] Chang S-Y A, Fefferman R. The Calderón-Zygmund decomposition on product domains. Amer J Math, 1982, 104:455-468 [5] Chang S-Y A, Fefferman R. Some recent developments in Fourier Analysis and Hp theory on product domains. Bull Amer Math Soc, 1985, 12:1-43 [6] Ding W, Lu G. Duality of multi-parameter Triebel-Lizorkin spaces associated with the composition of two singular integral operators. Tran Amer Math Soc, 2016, 368(10):7119-7152 [7] Fefferman R. Calderón-Zygmund theory for product domains-Hp spaces. Proc Nat Acad Sci, 1986, 83:840-843 [8] Fefferman R. Harmonic analysis on product spaces. Ann Math, 1987, 126:109-130 [9] Fefferman R, Stein E M. Singulsr integrals on product spaces. Adv Math, 1982, 45:117-143 [10] Ferguson S, Lacey M. A characterization of product BMO by commutators. Acta Math, 2002, 189(2):143-160 [11] Frazier M, Jawerth B. A discrete transform and decompositions of distribution spaces. J Funct Anal, 1990, 93:34-170 [12] García-Cuerva J, Rubio de Francia J. Weighted Norm Inequalities and Related Topics, North-Holland Math Stud, Vol 116. Amsterdam:North-Holland Publishing Co., 1985 [13] Grafakos L. Classical and Modern Fourier Analysis. Pearson Education, 2004 [14] Gundy R, Stein E M. Hp theory for the polydisk. Proc Nat Acad Sci, 1979, 76:1026-1029 [15] Han Y, Lin C, Lu G, et al. Hardy spaces associated with different homogeneities and boundedness of composition operators. Rev Mat Iberoam, 2013, 29(4):1127-1157 [16] Li B, Bownik M, Yang D, et al. Duality of weighted anisotropic Besov and Triebel-Lizorkin spaces. Positivity, 2012, 16(2):213-244 [17] Lu G, Ruan Z. Duality theory of weighted Hardy spaces with arbitrary number of parameters. Forum Math, 2014, 26(5):1429-1457 [18] Lu G, Zhu Y. Singular integrals and weighted Triebel-Lizorkin and Besov Spaces of arbitrary number of parameters. Acta Mathematica Sinica:English Series, 2013, 1:39-52 [19] Journe J L. Calderón-Zygmund operators on product spaces. Rev Mat Iberoam, 1985, 1:55-92 [20] Journe J L. Two problems of Calderón-Zygmund theory on product spaces. Ann Inst Fourier (Grenoble), 1988, 38:111-132 [21] Muscalu C, Pipher J, Tao T, et al. Multi-parameter paraproducts. Rev Mat Iberoam, 2006, 22:963-976 [22] Pipher J. Journer's covering lemma and its extension to higher dimensions. Duke Math J, 1986, 53:683-690 [23] Ruan Z. Weighted Hardy spaces in three-parameter case. J Math Anal Appl, 2010, 367(2):625-639 [24] Triebel H. Theory of Function Spaces. Birkhauser Verlag:Basel, 1983 [25] Cruz-Uribe D, Martell J, Pérez C. Sharp weighted estimates for classical operators. Adv Math, 2012, 229:408-441 [26] Xu J, Yang D. Applications of Herz-type Trebel-Lizorkin spaces. Acta Math Sci, 2003, 23B(3):328-338 [27] Yang D, Yuan W. A new class of function spaces connecting Triebel-Lizorkin spaces and Q spaces. J Funct Anal, 2008, 255(10):2760-2809 [28] Yang D, Yuan W. New Besov-type spaces and Triebel-Lizorkin type spaces including Q spaces. Math Z, 2010, 265(2):451-480 |
[1] | Min He, Maofa Wang, Jiale Chen. GENERALIZED COUNTING FUNCTIONS AND COMPOSITION OPERATORS ON WEIGHTED BERGMAN SPACES OF DIRICHLET SERIES [J]. Acta mathematica scientia,Series B, 2025, 45(2): 291-309. |
[2] | Jiecheng Chen, Shaolei Ru, Chenjing Wu. STRICHARTZ AND SMOOTHING ESTIMATES FOR DISPERSIVE SEMI-GROUP ${\rm e}^{-{\rm i} t P(D)}$ IN WEIGHTED ${ L}^{2}$ SPACES AND THEIR APPLICATIONS [J]. Acta mathematica scientia,Series B, 2025, 45(2): 401-415. |
[3] | Kaikai HAN, Yucheng LI, Maofa WANG. MULTIPLICATION OPERATORS ON WEIGHTED DIRICHLET SPACES [J]. Acta mathematica scientia,Series B, 2024, 44(6): 2225-2248. |
[4] | Lixia Feng, Yan Li, Zhiyu Wang, Liankuo Zhao. TOEPLITZ OPERATORS BETWEEN WEIGHTED BERGMAN SPACES OVER THE HALF-PLANE* [J]. Acta mathematica scientia,Series B, 2024, 44(5): 1707-1720. |
[5] | Zuoling Liu, Hasi Wulan. PRODUCT TYPE OPERATORS ACTING BETWEEN WEIGHTED BERGMAN SPACES AND BLOCH TYPE SPACES [J]. Acta mathematica scientia,Series B, 2024, 44(4): 1327-1336. |
[6] | 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. |
[7] | Ali Abkar. MEAN APPROXIMATION BY DILATATIONS IN BERGMAN SPACES ON THE UPPER HALF-PLANE* [J]. Acta mathematica scientia,Series B, 2023, 43(5): 2204-2214. |
[8] | Xiaohe Hu. COMPLEX SYMMETRIC $C_0$-SEMIGROUPS ON THE WEIGHTED HARDY SPACES $H_\gamma(\mathbb{D})$* [J]. Acta mathematica scientia,Series B, 2023, 43(5): 2121-2132. |
[9] | Zhuang Wang, Haiqing Xu. IMPROVED REGULARITY OF HARMONIC DIFFEOMORPHIC EXTENSIONS ON QUASIHYPERBOLIC DOMAINS* [J]. Acta mathematica scientia,Series B, 2023, 43(1): 373-386. |
[10] | Ruhan ZHAO. ON F(p,q,s) SPACES [J]. Acta mathematica scientia,Series B, 2021, 41(6): 1985-2020. |
[11] | Pengyan WANG, Pengcheng NIU. A PRIORI BOUNDS AND THE EXISTENCE OF POSITIVE SOLUTIONS FOR WEIGHTED FRACTIONAL SYSTEMS [J]. Acta mathematica scientia,Series B, 2021, 41(5): 1547-1568. |
[12] | Xiaomin WEI, Lining JIANG, Qiaoling XIN. THE FIELD ALGEBRA IN HOPF SPIN MODELS DETERMINED BY A HOPF *-SUBALGEBRA AND ITS SYMMETRIC STRUCTURE [J]. Acta mathematica scientia,Series B, 2021, 41(3): 907-924. |
[13] | Heng ZUO, Zhaohui SHEN, Guanglin RANG. HITTING PROBABILITIES OF WEIGHTED POISSON PROCESSES WITH DIFFERENT INTENSITIES AND THEIR SUBORDINATIONS [J]. Acta mathematica scientia,Series B, 2021, 41(1): 67-84. |
[14] | Huamei HUANG, Yujing GAO, Huiming ZHANG, Bo LI. WEIGHTED LASSO ESTIMATES FOR SPARSE LOGISTIC REGRESSION:NON-ASYMPTOTIC PROPERTIES WITH MEASUREMENT ERRORS [J]. Acta mathematica scientia,Series B, 2021, 41(1): 207-230. |
[15] | Gongbao LI, Tao YANG. THE EXISTENCE OF A NONTRIVIAL WEAK SOLUTION TO A DOUBLE CRITICAL PROBLEM INVOLVING A FRACTIONAL LAPLACIAN IN $\mathbb{R}^N$ WITH A HARDY TERM [J]. Acta mathematica scientia,Series B, 2020, 40(6): 1808-1830. |
|