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http://dx.doi.org/10.4134/BKMS.2015.52.4.1383

PRODUCT-TYPE OPERATORS FROM WEIGHTED BERGMAN-ORLICZ SPACES TO WEIGHTED ZYGMUND SPACES  

JIANG, ZHI-JIE (INSTITUTE OF NONLINEAR SCIENCE AND ENGINEERING COMPUTING SICHUAN UNIVERSITY OF SCIENCE AND ENGINEERING)
Publication Information
Bulletin of the Korean Mathematical Society / v.52, no.4, 2015 , pp. 1383-1399 More about this Journal
Abstract
Let ${\mathbb{D}}=\{z{\in}{\mathbb{C}}:{\mid}z{\mid}<1\}$ be the open unit disk in the complex plane $\mathbb{C}$, ${\varphi}$ an analytic self-map of $\mathbb{D}$ and ${\psi}$ an analytic function in $\mathbb{D}$. Let D be the differentiation operator and $W_{{\varphi},{\psi}}$ the weighted composition operator. The boundedness and compactness of the product-type operator $W_{{\varphi},{\psi}}D$ from the weighted Bergman-Orlicz space to the weighted Zygmund space on $\mathbb{D}$ are characterized.
Keywords
weighted Bergman-Orlicz spaces; product-type operators; weighted Zygmund spaces; boundedness; compactness;
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Times Cited By KSCI : 2  (Citation Analysis)
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1 R. F. Allen and F. Colonna, Weighted composition operators on the Bloch space of a bounded homogeneous domain, Topics in operator theory. Volume 1. Operators, matrices and analytic functions, 11-37, Oper. Theory Adv. Appl., 202, Birkhauser Verlag, Basel, 2010.
2 F. Colonna and S. Li, Weighted composition operators from the minimal Mobius invariant space into the Bloch space, Mediterr. J. Math. 10 (2013), no. 1, 395-409.   DOI
3 C. C. Cowen and B. D. MacCluer, Composition Operators on Spaces of Analytic Functions, CRC Press, 1995.
4 R. A. Hibschweiler and N. Portnoy, Composition followed by differentiation between Bergman and Hardy spaces, Rocky Mountain J. Math. 35 (2005), no. 3, 843-855.   DOI   ScienceOn
5 Z. J. Jiang, On a class of operators from weighted Bergman spaces to some spaces of analytic functions, Taiwanese J. Math. Soc. 15 (2011), no. 5, 2095-2121.   DOI
6 Z. J. Jiang, Weighted composition operators from weighted Bergman spaces to some spaces of analytic functions on the upper half plane, Util. Math. 93 (2014), 205-212.
7 S. Krantz and S. Stevic, On the iterated logarithmic Bloch space on the unit ball, Nonlinear Anal. TMA 71 (2009), no. 5-6, 1772-1795.   DOI   ScienceOn
8 P. Kumar and S. D. Sharma, Weighted composition operators from weighted Bergman Nevanlinna spaces to Zygmund spaces, Int. J. Modern Math. Sci. 3 (2012), no. 1, 31-54.
9 S. Li and S. Stevic, Weighted composition operators from Bergman-type spaces into Bloch spaces, Proc. Indian Acad. Sci. Math. Sci. 117 (2007), no. 3, 371-385.   DOI
10 S. Li and S. Stevic, Weighted composition operators from $H^{\infty}$ to the Bloch space on the polydisc, Abstr. Appl. Anal. 2007 (2007), Article ID 48478, 13 pages.
11 S. Li and S. Stevic, Composition followed by differentiation between Bloch type spaces, J. Comput. Anal. Appl. 9 (2007), no. 2, 195-205.
12 S. Li and S. Stevic, Products of composition and integral type operators from $H^{\infty}$ to the Bloch space, Complex Var. Elliptic Equ. 53 (2008), no. 5, 463-474.   DOI   ScienceOn
13 S. Li and S. Stevic, Weighted composition operators from Zygmund spaces into Bloch spaces, Appl. Math. Comput. 206 (2008), no. 2, 825-831.   DOI   ScienceOn
14 S. Li and S. Stevic, Composition followed by differentiation from mixed norm spaces to ${\alpha}$-Bloch spaces, Sb. Math. 199 (2008), no. 12, 1847-1857.   DOI   ScienceOn
15 S. Li and S. Stevic, Generalized composition operators on Zygmund spaces and Bloch type spaces, J. Math. Anal. Appl. 338 (2008), no. 2, 1282-1295.   DOI   ScienceOn
16 S. Li and S. Stevic, Composition followed by differentiation between $H^{\infty}$ and ${\alpha}$-Bloch spaces, Houston J. Math. 35 (2009), no. 1, 327-340.
17 L. Luo and S. Ueki, Weighted composition operators between weighted Bergman and Hardy spaces on the unit ball of ${\mathbb{C}}^n$, J. Math. Anal. Appl. 326 (2007), no. 1, 88-100.   DOI   ScienceOn
18 B. Sehba and S. Stevic, On some product-type operators from Hardy-Orlicz and Bergman-Orlicz spaces to weighted-type spaces, Appl. Math. Comput. 233 (2014), 565-581.   DOI   ScienceOn
19 L. Luo and S. Ueki, Compact weighted composition operators and multiplication operators between Hardy spaces, Abstr. Appl. Anal. 2008 (2008), Article ID 196498, 12 pages.
20 S. Ohno, Products of differentiation and composition on Bloch spaces, Bull. Korean Math. Soc. 46 (2009), no. 6, 1135-1140.   DOI   ScienceOn
21 A. K. Sharma, Products of multipication, composition and differentiation between Bergman and Bloch type spaces, Turkish J. Math. 35 (2011), no. 2, 275-291.
22 A. K. Sharma and Z. Abbas, Weighted composition operators between weighted Bergman-Nevanlinna and Bloch-type spaces, Appl. Math. Sci. 41 (2010), no. 4, 2039-2048.
23 S. Stevic, Essential norms of weighted composition operators from the ${\alpha}$-Bloch space to a weighted-type space on the unit ball, Abstr. Appl. Anal. 2008 (2008), Article ID 279691, 11 pages.
24 S. Stevic, On a new integral-type operator from the weighted Bergman space to the Blochtype space on the unit ball, Discrete Dyn. Nat. Soc. 2008 (2008), Article ID 154263, 14 pages.
25 S. Stevic, On a new operator from the logarithmic Bloch space to the Bloch-type space on the unit ball, Appl. Math. Comput. 206 (2008), no. 1, 313-320.   DOI   ScienceOn
26 S. Stevic, Norm of weighted composition operators from Bloch space to $H^{\infty}$ on the unit ball, Ars Combin. 88 (2008), 125-127.
27 S. Stevic, Norms of some operators from Bergman spaces to weighted and Bloch-type space, Util. Math. 76 (2008), 59-64.
28 S. Stevic, Products of composition and differentiation operators on the weighted Bergman space, Bull. Belg. Math. Soc. Simon Stevin 16 (2009), no. 4, 623-635.
29 S. Stevic, Norm and essential norm of composition followed by differentiation from ${\alpha}$-Bloch spaces to $H^{\infty}$, Appl. Math. Comput. 207 (2009), no. 1, 225-229.   DOI   ScienceOn
30 S. Stevic, On a new integral-type operator from the Bloch space to Bloch-type spaces on the unit ball, J. Math. Anal. Appl. 354 (2009), no. 2, 426-434.   DOI   ScienceOn
31 S. Stevic, Weighted composition operators from weighted Bergman spaces to weighted-type spaces on the unit ball, Appl. Math. Comput. 212 (2009), no. 2, 499-504.   DOI   ScienceOn
32 S. Stevic, Composition followed by differentiation from $H^{\infty}$ and the Bloch space to n-th weighted-type spaces on the unit disk, Appl. Math. Comput. 216 (2010), no. 12, 3450-3458.   DOI   ScienceOn
33 S. Stevic, On an integral operator between Bloch-type spaces on the unit ball, Bull. Sci. Math. 134 (2010), no. 4, 329-339.   DOI   ScienceOn
34 S. Stevic, Weighted composition operators from Bergman-Privalov-type spaces to weighted-type spaces on the unit ball, Appl. Math. Comput. 217 (2010), no. 5, 1939-1943.   DOI   ScienceOn
35 S. Stevic, Weighted differentiation composition operators from $H^{\infty}$ and Bloch spaces to n-th weighted-type spaces on the unit disk, Appl. Math. Comput. 216 (2010), no. 12, 3634-3641.   DOI   ScienceOn
36 S. Stevic and R. P. Agarwal, Weighted composition operators from logarithmic Blochtype spaces to Bloch-type spaces, J. Inequal. Appl. 2009 (2009), Article ID 964814, 21 pages.
37 W. Yang, Weighted composition operators from Bloch-type spaces to weighted-type spaces, Ars Combin. 93 (2009), 265-274.
38 S. Stevic, A. K. Sharma, and A. Bhat, Products of multiplication composition and differentiation operators on weighted Bergman spaces, Appl. Math. Comput. 217 (2011), no. 20, 8115-8125.   DOI   ScienceOn
39 S. Stevic, A. K. Sharma, and A. Bhat, Essential norm of product of multiplication composition and differentiation operators on weighted Bergman spaces, Appl. Math. Comput. 218 (2011), no. 6, 2386-2397.   DOI   ScienceOn
40 S. Stevic and S. I. Ueki, Integral-type operators acting between weighted-type spaces on the unit ball, Appl. Math. Comput. 215 (2009), no. 7, 2464-2471.   DOI   ScienceOn
41 W. Yang andW. Yan, Generalized weighted composition operators from area Nevanlinna spaces to weighted-type spaces, Bull. Korean Math. Soc. 48 (2011), no. 6, 1195-1205.   DOI   ScienceOn
42 K. Zhu, Spaces of Holomorphic Functions in the Unit Ball, Springer, New York, 2005.