全纯函数空间上几个量的等价刻画问题

Abstract

Abstract:

In this paper, the expression under the action of fractional derivative and fractional integral for a common function on the unit ball of several complex variables is improved. At the same time, the equivalent norms of the fractional differential on two holomorphic function spaces are improved, and the constraint conditions β=s+N for the fractional differential R^{s, t} and R^{β, t} in the equivalent norms are removed, where N is a positive integer.

Key words: Fractional derivative, Fractional integral, Equivalent characterization, Unit ball

CLC Number:

O174.56

Pengcheng Tang,Xuejun Zhang,Ruixin Lv. Equivalent Characterization of Several Quantities on Holomorphic Function Spaces[J].Acta mathematica scientia,Series A, 2019, 39(6): 1291-1299.

Trendmd

References 18

1	Zhu K H. Spaces of Holomorphic Functions in the Unit Ball. New York:Springer-Verlag, 2005
2	Rudin W. Function Theory in the Unit Ball of Cⁿ. New York:Springer-Verlag, 1980
3	黎深莲, 张学军, 徐思. Cⁿ中F(p, q, s)型空间上的Bergman型算子. 数学年刊, 2017, 38A (4): 375- 390
	Li S L , Zhang X J , Xu S . The Bergman type operators on the F(p, q, s) type spaces in Cⁿ. Chin Ann of Math, 2017, 38A (4): 375- 390
4	Ortega J , Fabrega J . Pointwise multipliers and Corona type decomposition in BMOA. Ann Inst Fourier (Grenoble), 1996, 46: 111- 137 doi: 10.5802/aif.1509
5	Ortega J , Fabrega J . Corona type decomposition in some Besov spaces. Math Scand, 1996, 78: 93- 111 doi: 10.7146/math.scand.a-12576
6	Zhang X J , Xiao J B , Hu Z J . The multipliers between the mixed norm space in Cⁿ. J Math Anal Appl, 2005, 311: 664- 674 doi: 10.1016/j.jmaa.2005.03.010
7	Liang Y X , Zhou Z H , Chen R Y . Product of extended Cesáro operator and composition operator from the logarithmic Bloch-type space to F(p, q, s) space on the unit ball. J Comput Anal Appl, 2013, 15: 432- 440
8	Liang Y X . On an integral-type operator from a weighted-type space to F(p, q, s) on the unit ball. Complex Var Ellip Equ, 2015, 60: 282- 291 doi: 10.1080/17476933.2014.926338
9	Ren G B , Shi J H . Bergman type operator on mixed norm space and applications. Chin Ann Math, 1997, 18B: 265- 276
10	Liu Y M . Boundedness of the Bergman type operators on mixed norm spaces. Proc Amer Math Soc, 2002, 130: 2363- 2367 doi: 10.1090/S0002-9939-02-06332-3
11	Ouyang C H , Yang W S , Zhao R H . Characterizations of Bergman spaces and Bloch space in the unit ball of Cⁿ. Trans Amer Math Soc, 1995, 347: 4301- 4319
12	Wulan H S . Compactness of the composition operators from the Bloch space B to Q_K spaces. Acta Math Sin, 2005, 21 (6): 1415- 1424 doi: 10.1007/s10114-005-0584-7
13	Zhang X J , Li S L , Shang Q L , Guo Y T . An integral estimate and the equivalent norms on F(p, q, s, k) spaces in the unit ball. Acta Math Sci, 2018, 38B (6): 1861- 1880
14	郭雨婷, 尚清丽, 张学军. 单位球上正规权Zygmund空间上的点乘子. 数学物理学报, 2018, 38A (6): 1041- 1048 doi: 10.3969/j.issn.1003-3998.2018.06.001
	Guo Y T , Shang Q L , Zhang X J . The pointwise multiplier on the normal weight Zygmund space in the unit ball. Acta Math Sci, 2018, 38A (6): 1041- 1048 doi: 10.3969/j.issn.1003-3998.2018.06.001
15	Li S L , Zhang X J , Xu S . The equivalent characterization of F(p, q, s) space on bounded symmetric domains of Cⁿ. Acta Math Sci, 2017, 37B (6): 1791- 1802
16	Li S L , Zhang X J , Xu S . The compact composition operator on the μ-Bergman space in the unit ball. Acta Math Sci, 2017, 37B (2): 425- 438
17	Zhang X J , Xi L H , Fan H X , Li J F . Atomic decomposition of μ-Bergman space in Cⁿ. Acta Math Sci, 2014, 34B (3): 779- 789
18	刘竟成, 李俊锋, 张学军. Cⁿ中单位球上Dirichlet型空间的Cesáro算子. 数学物理学报, 2015, 35A (1): 182- 193 doi: 10.3969/j.issn.0252-9602.2015.01.013
	Liu J C , Li J F , Zhang X J . Generalized Cesáro operator between different Dirichlet-type spaces in the unit ball of Cⁿ. Acta Math Sci, 2015, 35A (1): 182- 193 doi: 10.3969/j.issn.0252-9602.2015.01.013

[1]	Yao Wangjin, Zhang Huiping. Multiple Solutions for a Class of $\psi$-Caputo-Type Fractional Differential Equations with Instantaneous and Non-Instantaneous Impulses [J]. Acta mathematica scientia,Series A, 2025, 45(3): 807-823.
[2]	Lv Xueqin, He Songyan, Wang Shiyu. Combining RKM with FDM for Time Fractional Convection-Diffusion Equations with Variable Coefficients [J]. Acta mathematica scientia,Series A, 2025, 45(1): 153-164.
[3]	An Yanning, Liu Wenjun, Kong Aowen. Stability of Piezoelectric Beams with Magnetic Effects of Fractional Derivative Type and with/without Thermal Effects [J]. Acta mathematica scientia,Series A, 2023, 43(2): 355-376.
[4]	Meijuan Tan,Ying Huang,Xuejun Zhang. Another Discussion on the Pointwise Multiplier on the Normal Weight Zygmund Space in the Unit Ball [J]. Acta mathematica scientia,Series A, 2021, 41(6): 1616-1624.
[5]	Zaiyong Feng,Ning Chen,Yongpeng Tai,Zhengrong Xiang. On the Observer Design for Fractional Singular Linear Systems [J]. Acta mathematica scientia,Series A, 2021, 41(5): 1529-1544.
[6]	Xuanxuan Xi,Mimi Hou,Xianfeng Zhou. Invariance Sets and Well-Posedness for the Weak Solution of Non-Autonomous Caputo Fractional Evolution Equation [J]. Acta mathematica scientia,Series A, 2021, 41(1): 149-165.
[7]	Dexiang Ma,Abdullah Özbekler. Generalized Lyapunov Inequalities for a Higher-Order Sequential Fractional Differential Equation with Half-Linear Terms [J]. Acta mathematica scientia,Series A, 2020, 40(6): 1537-1551.
[8]	Pengcheng Tang,Si Xu,Xuejun Zhang. Bergman Type Operators on Logarithmic Weight General Function Spaces in Cⁿ [J]. Acta mathematica scientia,Series A, 2020, 40(5): 1151-1162.
[9]	Jingyun Lv,Xiaoyuan Yang. Approximate Controllability of Hilfer Fractional Integro-Differential Equations Using Sequence Method [J]. Acta mathematica scientia,Series A, 2020, 40(5): 1282-1294.
[10]	Yuji Liu. Solvability of BVPs for Impulsive Fractional Langevin Type Equations Involving Three Riemann-Liouville Fractional Derivatives [J]. Acta mathematica scientia,Series A, 2020, 40(1): 103-131.
[11]	Wenbing Sun,Qiong Liu. New Simpson Type Inequalities for Generalized Convex Functions on Fractal Space and Its Applications [J]. Acta mathematica scientia,Series A, 2018, 38(6): 1058-1066.
[12]	Yuting Guo,Qingli Shang,Xuejun Zhang. The Pointwise Multiplier on the Normal Weight Zygmund Space in the Unit Ball [J]. Acta mathematica scientia,Series A, 2018, 38(6): 1041-1048.
[13]	Huang Ziyan, Zhao Di, Li Hongyi. The Schwarz-Pick Lemma for Bounded Pluriharmonic Mappings in the Unit Ball of Cⁿ [J]. Acta mathematica scientia,Series A, 2018, 38(3): 433-445.
[14]	Zhao Yang, Peng Ru. Decomposition Theorems for F(p,q,s) Spaces on the Unit Ball of C_n [J]. Acta mathematica scientia,Series A, 2017, 37(3): 416-426.
[15]	Dong Xiaoyu, Bai Zhanbing, Sun Sujing. Positive Solutions for Some Boundary Value Problems with Conformable Fractional Differential Derivatives [J]. Acta mathematica scientia,Series A, 2017, 37(1): 82-91.

Equivalent Characterization of Several Quantities on Holomorphic Function Spaces

RichHTML

PDF (PC)

Abstract

Cite this article

share this article

References 18

Related Articles 15

Metrics

Comments

Recommended 10