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Extended Cesàro operators from logarithmic-type spaces to Bloch-type spaces. (English) Zbl 1168.47028

Summary: The boundedness and compactness of the extended Cesàro operator from logarithmic-type spaces to Bloch-type spaces on the unit ball are completely characterized in this paper.

MSC:

47B38 Linear operators on function spaces (general)
46E15 Banach spaces of continuous, differentiable or analytic functions
32A37 Other spaces of holomorphic functions of several complex variables (e.g., bounded mean oscillation (BMOA), vanishing mean oscillation (VMOA))
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References:

[1] D. D. Clahane and S. Stević, “Norm equivalence and composition operators between Bloch/Lipschitz spaces of the ball,” Journal of Inequalities and Applications, vol. 2006, Article ID 61018, 11 pages, 2006. · Zbl 1131.47018 · doi:10.1155/JIA/2006/61018
[2] S. Li and S. Stević, “Some characterizations of the Besov space and the \alpha -Bloch space,” Journal of Mathematical Analysis and Applications, vol. 346, no. 1, pp. 262-273, 2008. · Zbl 1156.32002 · doi:10.1016/j.jmaa.2008.05.044
[3] S. Li and H. Wulan, “Characterizations of \alpha -Bloch spaces on the unit ball,” Journal of Mathematical Analysis and Applications, vol. 343, no. 1, pp. 58-63, 2008. · Zbl 1204.32006 · doi:10.1016/j.jmaa.2008.01.023
[4] K. Zhu, Spaces of Holomorphic Functions in the Unit Ball, vol. 226 of Graduate Texts in Mathematics, Springer, New York, NY, USA, 2005. · Zbl 1067.32005
[5] S. Stević, “On a new operator from the logarithmic Bloch space to the Bloch-type space on the unit ball,” Applied Mathematics and Computation, vol. 206, no. 1, pp. 313-320, 2008. · Zbl 1162.47029 · doi:10.1016/j.amc.2008.09.002
[6] K. H. Zhu, “Multipliers of BMO in the Bergman metric with applications to Toeplitz operators,” Journal of Functional Analysis, vol. 87, no. 1, pp. 31-50, 1989. · Zbl 0705.47025 · doi:10.1016/0022-1236(89)90003-7
[7] X. Fu and X. Zhu, “Weighted composition operators on some weighted spaces in the unit ball,” Abstract and Applied Analysis, vol. 2008, Article ID 605807, 8 pages, 2008. · Zbl 1160.47024 · doi:10.1155/2008/605807
[8] D. Girela, J. Á. Peláez, F. Pérez-González, and J. Rättyä, “Carleson measures for the Bloch space,” Integral Equations and Operator Theory, vol. 61, no. 4, pp. 511-547, 2008. · Zbl 1185.30056 · doi:10.1007/s00020-008-1602-9
[9] Ch. Pommerenke, “Schlichte Funktionen und analytische Funktionen von beschränkter mittlerer Oszillation,” Commentarii Mathematici Helvetici, vol. 52, no. 4, pp. 591-602, 1977. · Zbl 0369.30012 · doi:10.1007/BF02567392
[10] A. Aleman and J. A. Cima, “An integral operator on Hp and Hardy/s inequality,” Journal d/Analyse Mathématique, vol. 85, pp. 157-176, 2001. · Zbl 1061.30025 · doi:10.1007/BF02788078
[11] A. G. Siskakis and R. Zhao, “A Volterra type operator on spaces of analytic functions,” in Function Spaces, vol. 232 of Contemporary Mathematics, pp. 299-311, American Mathematical Society, Providence, RI, USA, 1999. · Zbl 0955.47029
[12] S. Li and S. Stević, “Generalized composition operators on Zygmund spaces and Bloch type spaces,” Journal of Mathematical Analysis and Applications, vol. 338, no. 2, pp. 1282-1295, 2008. · Zbl 1135.47021 · doi:10.1016/j.jmaa.2007.06.013
[13] S. Li and S. Stević, “Products of composition and integral type operators from H\infty to the Bloch space,” Complex Variables and Elliptic Equations, vol. 53, no. 5, pp. 463-474, 2008. · Zbl 1159.47019 · doi:10.1080/17476930701754118
[14] S. Li and S. Stević, “Products of Volterra type operator and composition operator from H\infty and Bloch spaces to Zygmund spaces,” Journal of Mathematical Analysis and Applications, vol. 345, no. 1, pp. 40-52, 2008. · Zbl 1145.47022 · doi:10.1016/j.jmaa.2008.03.063
[15] S. Li and S. Stević, “Products of integral-type operators and composition operators between Bloch-type spaces,” Journal of Mathematical Analysis and Applications, vol. 349, no. 2, pp. 596-610, 2009. · Zbl 1155.47036 · doi:10.1016/j.jmaa.2008.09.014
[16] S. Stević, “Norms of some operators from Bergman spaces to weighted and Bloch-type spaces,” Utilitas Mathematica, vol. 76, pp. 59-64, 2008. · Zbl 1160.47027
[17] D.-C. Chang, S. Li, and S. Stević, “On some integral operators on the unit polydisk and the unit ball,” Taiwanese Journal of Mathematics, vol. 11, no. 5, pp. 1251-1285, 2007. · Zbl 1149.47026
[18] D.-C. Chang and S. Stević, “Estimates of an integral operator on function spaces,” Taiwanese Journal of Mathematics, vol. 7, no. 3, pp. 423-432, 2003. · Zbl 1052.47044
[19] S. Stević, “Cesàro averaging operators,” Mathematische Nachrichten, vol. 248-249, no. 1, pp. 185-189, 2003. · Zbl 1024.47014 · doi:10.1002/mana.200310013
[20] S. Stević, “Boundedness and compactness of an integral operator on a weighted space on the polydisc,” Indian Journal of Pure and Applied Mathematics, vol. 37, no. 6, pp. 343-355, 2006. · Zbl 1121.47032
[21] S. Stević, “Boundedness and compactness of an integral operator in a mixed norm space on the polydisk,” Sibirskiĭ Matematicheskiĭ Zhurnal, vol. 48, no. 3, pp. 694-706, 2007. · Zbl 1164.47331
[22] K. Avetisyan and S. Stević, “Extended Cesàro operators between different Hardy spaces,” Applied Mathematics and Computation, vol. 207, no. 2, pp. 346-350, 2009. · Zbl 1163.32004 · doi:10.1016/j.amc.2008.10.055
[23] Z. Hu, “Extended Cesàro operators on mixed norm spaces,” Proceedings of the American Mathematical Society, vol. 131, no. 7, pp. 2171-2179, 2003. · Zbl 1054.47023 · doi:10.1090/S0002-9939-02-06777-1
[24] Z. Hu, “Extended Cesáro operators on the Bloch space in the unit ball of \Bbb Cn,” Acta Mathematica Scientia. Series B, vol. 23, no. 4, pp. 561-566, 2003. · Zbl 1044.47023
[25] Z. Hu, “Extended Cesàro operators on Bergman spaces,” Journal of Mathematical Analysis and Applications, vol. 296, no. 2, pp. 435-454, 2004. · Zbl 1072.47029 · doi:10.1016/j.jmaa.2004.01.045
[26] S. Li, “Riemann-Stieltjes operators from F(p,q,s) spaces to \alpha -Bloch spaces on the unit ball,” Journal of Inequalities and Applications, vol. 2006, Article ID 27874, 14 pages, 2006. · Zbl 1131.47030 · doi:10.1155/JIA/2006/27874
[27] S. Li and S. Stević, “Integral type operators from mixed-norm spaces to \alpha -Bloch spaces,” Integral Transforms and Special Functions, vol. 18, no. 7-8, pp. 485-493, 2007. · Zbl 1131.47031 · doi:10.1080/10652460701320703
[28] S. Li and S. Stević, “Riemann-Stieltjes operators on Hardy spaces in the unit ball of \Bbb Cn,” Bulletin of the Belgian Mathematical Society. Simon Stevin, vol. 14, no. 4, pp. 621-628, 2007. · Zbl 1136.47023
[29] S. Li and S. Stević, “Riemann-Stieltjes-type integral operators on the unit ball in \Bbb Cn,” Complex Variables and Elliptic Equations, vol. 52, no. 6, pp. 495-517, 2007. · Zbl 1124.47022 · doi:10.1080/17476930701235225
[30] S. Li and S. Stević, “Compactness of Riemann-Stieltjes operators between F(p,q,s) spaces and \alpha -Bloch spaces,” Publicationes Mathematicae Debrecen, vol. 72, no. 1-2, pp. 111-128, 2008. · Zbl 1164.47040
[31] S. Li and S. Stević, “Riemann-Stieltjes operators between different weighted Bergman spaces,” Bulletin of the Belgian Mathematical Society. Simon Stevin, vol. 15, no. 4, pp. 677-686, 2008. · Zbl 1169.47026
[32] S. Li and S. Stević, “Riemann-Stieltjes operators between mixed norm spaces,” Indian Journal of Mathematics, vol. 50, no. 1, pp. 177-188, 2008. · Zbl 1159.47012
[33] S. Li and S. Stević, “Cesàro-type operators on some spaces of analytic functions on the unit ball,” Applied Mathematics and Computation, vol. 208, no. 2, pp. 378-388, 2009. · Zbl 1166.45009 · doi:10.1016/j.amc.2008.12.006
[34] S. Stević, “On an integral operator on the unit ball in \Bbb Cn,” Journal of Inequalities and Applications, vol. 2005, no. 1, pp. 81-88, 2005. · Zbl 1074.47013 · doi:10.1155/JIA.2005.81
[35] X. Tang, “Extended Cesàro operators between Bloch-type spaces in the unit ball of \Bbb Cn,” Journal of Mathematical Analysis and Applications, vol. 326, no. 2, pp. 1199-1211, 2007. · Zbl 1117.47022 · doi:10.1016/j.jmaa.2006.03.082
[36] J. Xiao, “Riemann-Stieltjes operators on weighted Bloch and Bergman spaces of the unit ball,” Journal of the London Mathematical Society. Second Series, vol. 70, no. 1, pp. 199-214, 2004. · Zbl 1064.47034 · doi:10.1112/S0024610704005484
[37] S. Stević, “Compactness of the Hardy-Littlewood operator on some harmonic function spaces,” Siberian Mathematical Journal, vol. 50, no. 1, pp. 167-180, 2009. · Zbl 1222.47048 · doi:10.1007/s11202-009-0019-2
[38] S. Stević, “On a new operator from H\infty to the Bloch-type space on the unit ball,” Utilitas Mathematica, vol. 77, pp. 257-263, 2008. · Zbl 1155.32002 · doi:10.1155/2008/154263
[39] S. Stević, “On a new integral-type operator from the weighted Bergman space to the Bloch-type space on the unit ball,” Discrete Dynamics in Nature and Society, vol. 2008, Article ID 154263, 14 pages, 2008. · Zbl 1155.32002 · doi:10.1155/2008/154263
[40] K. Madigan and A. Matheson, “Compact composition operators on the Bloch space,” Transactions of the American Mathematical Society, vol. 347, no. 7, pp. 2679-2687, 1995. · Zbl 0826.47023 · doi:10.2307/2154848
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