Riemann–Stieltjes Operator from the General Space to Zygmund-Type Spaces on the Unit Ball
详细信息 查看全文
- 作者：Yongmin Liu ; Yanyan Yu ; Xiaoman Liu
- 关键词：Unit ball ; General space ; Zygmund ; type space ; Riemann–Stieltjes operator ; Primary 47B38 ; Secondary 47G10 ; 32A10 ; 32A18
- 刊名：Complex Analysis and Operator Theory
- 出版年：2015
- 出版时间：June 2015
- 年：2015
- 卷：9
- 期：5
- 页码：985-997
- 全文大小：466 KB
- 参考文献：1.Bierstedt, K., Summers, W.: Biduals of weighted Banach spaces of analytic functions. J. Aust. Math. Soc. (Ser. A) 54, 70-9 (1993)View Article MATH MathSciNet
2.Chen, H.: \(\alpha \) -Bloch functions and Lipschitz classes. Acta Math. Sinica Engl. Ser. 28(11), 2355-364 (2012)View Article MATH
3.Fang, Z., Zhou, Z.: Isometric composition operators on the Bloch type space in the polydisk (in Chinese). Acta Math. Sinica (Chin. Ser.) 55(3), 273-80 (2012)MATH MathSciNet
4.Hu, Z.: Extended Cesàro operators on mixed norm spaces. Proc. Am. Math. Soc. 131(7), 2171-179 (2003). (electronic)
5.Hu, Z., Liu, Y., Zhang, X.: Pointwise multipliers from \(F(p, q, s)\) spaces to \(\mu \) -Bloch spaces on the unit ball (in Chinese). Appl. Math. J. Chin. Univ. Ser. A 25(3), 326-32 (2010)MathSciNet
6.Li, S., Stevi?, S.: Generalized composition operators on Zygmund spaces and Bloch type spaces. J. Math. Anal. Appl. 338(2), 1282-295 (2008)View Article MATH MathSciNet
7.Li, S., Stevi?, S.: Compactness of Riemann–Stieltjes operators between \(F(p, q, s)\) and \(\alpha \) -Bloch spaces. Publ. Math. Debr. 72(1/2), 111-28 (2008)MATH
8.Li, S., Stevi?, S.: Products of Volterra type operator and composition operator from \(H^\infty \) and Bloch spaces to Zygmund spaces. J. Math. Anal. Appl. 345(1), 40-2 (2008)View Article MATH MathSciNet
9.Li, S., Stevi?, S.: Cesàro type operators on some spaces of analytic functions on the unit ball. Appl. Math. Comput. 208(2), 378-88 (2009)
10.Li, B., Ouyang, C.: Higher radial derivative of Bloch type functions. Acta Math. Sci. Ser. B 22(4), 433-45 (2002)MATH MathSciNet
11.Li, S., Wulan, H.: Volterra type operators on \(Q_K\) spaces. Taiwan. J. Math. 14(1), 195-11 (2010)MATH MathSciNet
12.Liang, Y., Zhou, Z.: Product of extended Cesàro operator and composition operator from Lipschitz space to \(F(p, q, s)\) space on the unit ball. Abstr. Appl. Anal. 2011, Art ID 152635 (2011)
13.Liu, X., Yu, Y.: The product of differentiation operator and multiplication operator from \(H^\infty \) to Zygmund spaces. J. Xuzhou Norm. Univ. Natl. Sci. Ed. 29(1), 37-9 (2011)MATH
14.Liu, Y., Yu, Y.: On an integral-type operator from mixed norm spaces to Zygmund-type spaces on the unit ball (in Chinese). Acta Math. Sinica (Chin. Ser.) 56(3), 381-90 (2013)MATH MathSciNet
15.Liu, Y., Zhou, J.: On an operator \(M_u{\cal {R}}\) from mixed norm spaces to Zygmund-type spaces on the unit ball. Complex. Anal. Oper. Theory 7(1), 593-06 (2013)View Article MATH MathSciNet
16.Lv, X., Tang, X.: Extended Cesàro operators from \(F(p, q, s)\) spaces to Bloch-type spaces in the unit ball. Commun. Korean Math. Soc. 24(1), 57-6 (2009)
17.Rudin, W.: Function Theory in the Unit Ball of \( \mathbb{C}^n\) . Springer, New York, Berlin (1980)View Article
18.Stevi?, S.: Boundedness and compactness of an integral operator in a mixed norm space on the polydisc. Sib. Math. J. 48(3), 559-69 (2007)View Article
19.Stevi?, S.: On a new operator from \(H^\infty \) to the Bloch-type space on the unit ball. Util. Math. 77, 257-63 (2008)MATH MathSciNet
20.Stevi?, S.: Norm of weighted composition operators from Bloch space to \(H_\mu ^\infty \) on the unit ball. Ars Comb. 88, 125-27 (2008)MATH
21.Stevi?, S.: On an integral-type operator from logarithmic Bloch-type and mixed-norm spaces to Bloch-type spaces. Nonlinear Anal. 71(12), 6323-342 (2009)View Article MATH MathSciNet
22.Stevi?, S.: On a new integral-type operator from the Bloch space to Bloch-type spaces on the unit ball. J. Math. Anal. Appl. 354(2), 426-34 (2009)View Article MATH MathSciNet
23.Stevi?, S.: On operator \(L^g_\varphi \) from the logarithmic Bloch-type space to the mixed-norm space on the unit ball. Appl. Math. Comput. 215(12), 4248-255 (2010)View Article MATH MathSciNet
24.Stevi?, S.: On an integral operator between Bloch-type spaces on the unit ball. Bull. Sci. Math. 134(4), 329-39 (2010)View Article MATH MathSciNet
25.Stevi?, S.: Weighted iterated radial composition operators between some spaces of holomorphic functions on the unit ball. Abstr. Appl. Anal. 2010, Art ID 801264 (2010)
26.Stevi?, S.: On some integral-type operators between a general space and Bloch-type spaces. Appl. Math. Comput. 218(6), 2600-618 (2011)View Article MATH MathSciNet
27.Stevi?, S.: Boundedness and compactness of an integral-type operator from Bloch-type spaces with normal weights to \(F(p, q, s)\) space. Appl. Math. Comput. 218(9), 5414-421 (2012)View Article MATH MathSciNet
28.Ueki, S.I.: On the Li-Stevi? integral type operators from weighted Bergman spaces into \(\beta \) -Zygmund spaces. Integr. Equ. Oper. Theory 74(1), 137-50 (2012)View Article MATH MathSciNet
29.Yang, C.: Integral-type operators from \(F(p, q, s)\) spaces to Zygmund-type spaces on the unit ball. J. Inequal. Appl. 2010, Art ID 789285 (2010)
30.Yang, W.: Composition operators from \(F(p, q, s)\) spaces to the - 作者单位：Yongmin Liu (1)
Yanyan Yu (2)
Xiaoman Liu (3)
1. School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou?, 221116, People’s Republic of China
2. School of Mathematics and Physics Science, Xuzhou Institute of Technology, Xuzhou?, 221111, People’s Republic of China
3. School of Science, Communication University of China, Beijing?, 100024, People’s Republic of China - 刊物类别：Mathematics and Statistics
- 刊物主题：Mathematics
Mathematics
Operator Theory
Analysis - 出版者：Birkh盲user Basel
- ISSN：1661-8262
文摘
In this paper, the authors characterize the boundedness and compactness of Riemann–Stieltjes operator from the general space \(F(p, q, s)\) to Zygmund-type spaces \({\mathcal Z}_{\mu }\) on the unit ball and some necessary and sufficient conditions of the Riemann–Stieltjes operator to be bounded and compact are obtained.