Weighted differentiation composition operators from the logarithmic Bloch space to the weighted-type space

[1] J. Arazy, Multipliers of Bloch functions, University of Haifa Mathematics Publication 54 1982.Search in Google Scholar

[2] K. D. Bierstedt and W. H. Summers, Biduals of weighted Banach spaces of analytic functions, J. Austral. Math. Soc. (Series A) 54 (1993), 70-79.10.1017/S1446788700036983Search in Google Scholar

[3] D. C. Chang, S. Li and S. Stević, On some integral operators on the unit polydisk and the unit ball, Taiwanese J. Math. 11 (5) (2007), 1251-1286.10.11650/twjm/1500404862Search in Google Scholar

[4] F. Colonna and S. Li, Weighted composition operators from Hardy spaces into logarithmic Bloch spaces, J. Funct. Spaces Appl. Volume 2012, Article ID 454820, 20 pages.10.1155/2012/454820Search in Google Scholar

[5] C. Cowen and B. MacCluer, Composition operators on spaces of analytic functions, CRC Press, Boca Raton, FL, 1995.Search in Google Scholar

[6] P. Galindo and M. Lindström and S. Stević, Essential norm of operators into weighted-type spaces on the unit ball, Abstr. Appl. Anal. Vol. 2011, Article ID 939873, (2011), 13 pages.10.1155/2011/939873Search in Google Scholar

[7] J. Han and Y. Wu, The high order derivative characterization of logarithmic Bloch type spaces, J. Anhui Univ. Sci. Tech. 2 (2013), 32-34.Search in Google Scholar

[8] Z. J. Jiang, On a product operator from weighted Bergman-Nevanlinna spaces to weighted Zygmund spaces, J. Inequal. Appl. Vol. 2014, Article no. 404, (2014), 14 pages.10.1186/1029-242X-2014-404Search in Google Scholar

[9] Z. J. Jiang, On Stević-Sharma operator from the Zygmund space to the Bloch-Orlicz space, Adv. Difference Equ. Vol. 2015, Article ID 228, (2015), 12 pages.10.1186/s13662-015-0567-7Search in Google Scholar

[10] S. Krantz and S. Stević, On the iterated logarithmic Bloch space on the unit ball, Nonlinear Anal. TMA 71 (2009), 1772-1795.10.1016/j.na.2009.01.013Search in Google Scholar

[11] H. Li and X. Fu, A new characterization of generalized weighted composition operators from the Bloch space into the Zygmund space, J. Funct. Spaces Appl. Volume 2013, Article ID 925901, 12 pages.10.1155/2013/925901Search in Google Scholar

[12] H. H. Li and Z. Guo, On a product-type operator from Zygmund-type spaces to Bloch-Orlicz spaces J. Inequal. Appl. Vol. 2015, Article no. 132, (2015), 18 pages.10.1186/s13660-015-0658-8Search in Google Scholar

[13] S. Li and S. Stević, Composition followed by differentiation between Bloch type spaces, J. Comput. Anal. Appl. 9 (2007), 195-205.Search in Google Scholar

[14] S. Li and S. Stević, Composition followed by differentiation from mixednorm spaces to α-Bloch spaces, Sb. Math 199 (12) (2008), 1847-1857.10.1070/SM2008v199n12ABEH003983Search in Google Scholar

[15] S. Li and S. Stević, Generalized composition operators on Zygmund spaces and Bloch type spaces, J. Math. Anal. Appl. 338 (2008), 1282-1295.10.1016/j.jmaa.2007.06.013Search in Google Scholar

[16] S. Li and S. Stević, Products of composition and integral type operators from H^∞ to the Bloch space, Complex Var. Elliptic Equ. 53 (5) (2008), 463-474.10.1080/17476930701754118Search in Google Scholar

[17] S. Li and S. Stević, Composition followed by differentiation between H^∞ and α-Bloch spaces, Houston J. Math. 35 (2009), 327-340.Search in Google Scholar

[18] S. Li and S. Stević, Products of composition and differentiation operators from Zygmund spaces to Bloch spaces and Bers spaces, Appl. Math. Comput. 217 (2010), 3144-3154.Search in Google Scholar

[19] S. Li and S. Stević, Generalized weighted composition operators from α-Bloch spaces into weighted-type spaces, J. Inequal. Appl. Vol. 2015, Article No. 265, (2015), 12 pages.10.1186/s13660-015-0770-9Search in Google Scholar

[20] Y. X. Liang and X. T. Dong, New characterizations for the products of differentiation and composition operators between Bloch-type spaces, J. Inequal. Appl. Vol. 2014, Article No. 502, (2014), 14 pages.10.1186/1029-242X-2014-502Open DOISearch in Google Scholar

[21] Y. Liu and Y. Yu, On a Stević-Sharma operator from Hardy spaces to the logarithmic Bloch spaces, J. Inequal. Appl. Vol. 2015, Article no. 22, (2015), 19 pages.10.1186/s13660-015-0547-1Search in Google Scholar

[22] J. Long, C. Qiu and P.Wu, Weighted composition followed and proceeded by differentiation operators from Zygmund spaces to Bloch-type spaces, J. Inequal. Appl. Vol. 2014, Article No. 152, (2014), 12 pages.10.1186/1029-242X-2014-152Open DOISearch in Google Scholar

[23] K. Madigan and A. Matheson, Compact composition operators on the Bloch space, Trans. Amer. Math. Soc. 347 (1995), 2679-2687.10.1090/S0002-9947-1995-1273508-XSearch in Google Scholar

[24] A. Montes-Rodriguez, The essential norm of a composition operator on Bloch spaces, Pacific J. Math. 188 (1999), 339-351.10.2140/pjm.1999.188.339Search in Google Scholar

[25] S. Ohno, Products of differentiation and composition on Bloch spaces, Bull. Korean Math. Soc. 46 (6) (2009), 1135-1140.10.4134/BKMS.2009.46.6.1135Open DOISearch in Google Scholar

[26] V. Rădulescu, Qualitative Analysis of Nonlinear Elliptic Partial Differential Equations: Monotonicity, Analytic, and Variational Methods, Contemporary Mathematics and Its Applications, vol. 6, Hindawi Publ. Corp., 2008.10.1155/9789774540394Search in Google Scholar

[27] B. Sehba and S. Stević, On some product-type operators from Hardy-Orlicz and Bergman-Orlicz spaces to weighted-type spaces, Appl. Math. Comput. 233C (2014), 565-581.10.1016/j.amc.2014.01.002Search in Google Scholar

[28] A. G. Siskakis and R. Zhao, A Volterra type operator on spaces of analytic functions, Contemp. Math. 232 (1999), 299-311.10.1090/conm/232/03406Search in Google Scholar

[29] S. Stević, Generalized composition operators from logarithmic Bloc spaces to mixed-norm spaces, Util. Math. 77 (2008), 167-172.Search in Google Scholar

[30] S. Stević, On a new integral-type operator from the weighted Bergman space to the Bloch-type space on the unit ball, Discrete Dyn. Nat. Soc. Vol. 2008, Article ID 154263, (2008), 14 pages.10.1155/2008/154263Search in Google Scholar

[31] S. Stević, On a new operator from the logarithmic Bloch space to the Bloch-type space on the unit ball, Appl. Math. Comput. 206 (2008), 313-320.Search in Google Scholar

[32] S. Stević, Integral-type operators from a mixed norm space to a Blochtype space on the unit ball, Siberian Math. J. 50 (6) (2009), 1098-1105.10.1007/s11202-009-0121-5Search in Google Scholar

[33] S. Stević, Norm and essential norm of composition followed by differentiation from α-Bloch spaces to H^∞_μ, Appl. Math. Comput. 207 (2009), 225-229.Search in Google Scholar

[34] S. Stević, On an integral-type operator from logarithmic Bloch-type and mixed-norm spaces to Bloch-type spaces, Nonlinear Anal. TMA 71 (2009), 6323-6342.10.1016/j.na.2009.06.087Search in Google Scholar

[35] S. Stević, Products of composition and differentiation operators on the weighted Bergman space, Bull. Belg. Math. Soc. Simon Stevin, 16 (2009), 623-635.10.36045/bbms/1257776238Search in Google Scholar

[36] S. Stević, Products of integral-type operators and composition operators from the mixed norm space to Bloch-type spaces, Siberian Math. J. 50 (4) (2009), 726-736.10.1007/s11202-009-0083-7Search in Google Scholar

[37] S. Stević, Weighted differentiation composition operators from mixednorm spaces to weighted-type spaces, Appl. Math. Comput. 211 (2009), 222-233.Search in Google Scholar

[38] S. Stević, Composition followed by differentiation from H^∞ and the Bloch space to nth weighted-type spaces on the unit disk, Appl. Math. Comput. 216 (2010), 3450-3458.Search in Google Scholar

[39] S. Stević, On an integral-type operator from logarithmic Bloch-type spaces to mixed-norm spaces on the unit ball, Appl. Math. Comput. 215 (2010), 3817-3823.Search in Google Scholar

[40] S. Stević, On operator Pg ϕ from the logarithmic Bloch-type space to the mixed-norm space on unit ball, Appl. Math. Comput. 215 (2010), 4248-4255.Search in Google Scholar

[41] S. Stević, Weighted differentiation composition operators from H^∞ and Bloch spaces to nth weigthed-type spaces on the unit disk, Appl. Math. Comput. 216 (2010), 3634-3641.Search in Google Scholar

[42] S. Stević, Weighted differentiation composition operators from mixednorm spaces to the nth weighted-type space on the unit disk, Abstr. Appl. Anal. Vol. 2010, Article ID 246287, (2010), 15 pages.10.1155/2010/246287Search in Google Scholar

[43] S. Stević, Characterizations of composition followed by differentiation between Bloch-type spaces, Appl. Math. Comput. 218 (2011), 4312-4316.Search in Google Scholar

[44] S. Stević, On some integral-type operators between a general space and Bloch-type spaces, Appl. Math. Comput. 218 (2011), 2600-2618.Search in Google Scholar

[45] S. Stević, Weighted iterated radial operators between different weighted Bergman spaces on the unit ball, Appl. Math. Comput. 218 (2012), 8288-8294.Search in Google Scholar

[46] S. Stević and A. K. Sharma, Iterated differentiation followed by composition from Bloch-type spaces to weighted BMOA spaces, Appl. Math. Comput. 218 (2011), 3574-3580.Search in Google Scholar

[47] S. Stević, A. K. Sharma and A. Bhat, Products of multiplication composition and differentiation operators on weighted Bergman spaces, Appl. Math. Comput. 217 (2011), 8115-8125.Search in Google Scholar

[48] S. Stević, A. K. Sharma and A. Bhat, Essential norm of products of multiplication composition and differentiation operators on weighted Bergman spaces, Appl. Math. Comput. 218 (2011), 2386-2397.Search in Google Scholar

[49] S. Stević, A. K. Sharma and S. D. Sharma, Generalized integration operators from the space of integral transforms into Bloch-type spaces, J. Comput. Anal. Appl. 14 (6) (2012), 1139-1147.Search in Google Scholar

[50] S. Stević and S. I. Ueki, Integral-type operators acting between weightedtype spaces on the unit ball, Appl. Math. Comput. 215 (2009), 2464-2471.Search in Google Scholar

[51] H. Wulan, D. Zheng and K. Zhu, Compact composition operators on BMOA and the Bloch space, Proc. Amer. Math. Soc. 137 (2009), 3861-3868.10.1090/S0002-9939-09-09961-4Search in Google Scholar

[52] R. Zhao, Essential norms of composition operators between Bloch type spaces, Proc. Amer. Math. Soc. 138 (2010), 2537-2546.10.1090/S0002-9939-10-10285-8Search in Google Scholar

[53] J. Zhou and X. Zhu, Product of differentiation and composition operators on the logarithmic Bloch space, J. Ineq. Appl. Vol. 2014, Article No. 453, (2014), 12 pages.10.1186/1029-242X-2014-453Search in Google Scholar

[54] K. Zhu, Bloch type spaces of analytic functions, Rocky Mountain J. Math. 23 (1993), 1143-1177.10.1216/rmjm/1181072549Search in Google Scholar

[55] X. Zhu, Products of differentiation, composition and multiplication from Bergman type spaces to Bers type space, Integ. Tran. Spec. Funct. 18 (2007), 223-231.10.1080/10652460701210250Search in Google Scholar

[56] X. Zhu, Generalized weighted composition operators on weighted Bergman spaces, Numer. Funct. Anal. Opt. 30 (2009), 881-893.10.1080/01630560903123163Open DOISearch in Google Scholar

[57] X. Zhu, Generalized weighted composition operators on Bloch-type spaces, J. Inequal. Appl. Vol. 2015, Article no. 59, (2015), 9 pages.10.1186/s13660-015-0580-0Search in Google Scholar