黃成世 江治杰
Then the operator ?S ?u → ,φ,m:A p α→H ∞ μ ?is metrically compact and (66) holds if and only if the operators ?M ?u iC φ R ?i:A p α→H ∞ μ ?are metrically compact for ?i= 0,m ?.
References:
[1] ??Li S X, Stevi ?S. Composition followed by differentiation between Bloch type spaces [J]. J Comput Anal Appl, 2007, 9: 195.
[2] ?Li S X, Stevi ?S. Composition followed by differentiation from mixed norm spaces to ?α -Bloch spaces [J]. Sb Math, 2008, 199: 1847.
[3] ?Li S X, Stevi ?S. Composition followed by differentiation between ?H ∞ ?and ?α -Bloch spaces [J]. Houston J Math, 2009, 35: 327.
[4] ?Li S X, Stevi ?S. Products of composition and differentiation operators from Zygmund spaces to Bloch spaces and Bers spaces [J]. Appl Math Comput, 2010, 217: 3144.
[5] ?Stevi ?S. Norm and essential norm of composition followed by differentiation from ?α -Bloch spaces to ?H ∞ μ ?[J]. Appl Math Comput, 2009, 207: 225.
[6] ?Stevi ?S. Products of composition and differentiation operators on the weighted Bergman space [J]. B Belg Math Soc-Sim, 2009, 16: 623.
[7] ?Stevi ?S. Composition followed by differentiation from ?H ∞ ?and the Bloch space to ?n th weighted-type spaces on the unit disk [J]. Appl Math Comput, 2010, 216: 3450.
[8] ?Hibschweiler R A, Portnoy N. Composition followed by differentiation between Bergman and Hardy spaces [J]. Rocky Mt J Math: 2005, 35: 843.
[9] ?Ohno S. Products of composition and differentiation on Bloch spaces [J]. Bull Korean Math Soc, 2009, 46: 1135.
[10] ?Stevi ?S, Sharma A K, Bhat A. Essential norm of multiplication composition and differentiation operators on weighted Bergman spaces [J]. Appl Math Comput, 2011, ?218: 2386.
[11] Stevi ?S, Sharma A K, Bhat A. Products of multiplication composition and differentiation operators on weighted Bergman spaces [J]. Appl Math Comput, 2011, 217: 8115.
[12] Sharma A K. Products of composition multiplication and differentiation between Bergman and Bloch type spaces [J]. Turkish J Math, 2011, 35: 275.
[13] Jiang Z J. Product-type operators from Logarithmic Bergman-type spaces to Zygmund-Orlicz spaces [J]. Mediterr J Math, 2016, 13: 4639.
[14] Jiang Z J. Product-type operators from Zygmund spaces to Bloch-Orlicz spaces [J]. Complex Var Elliptic, 2017, 62: 1645.
[15] Wang S M, Wang M F, Guo X. Products of composition, multiplication and iterated differentiation operators between Banach Spaces of holomorphic functions [J]. Taiwan J Math, 2020, 24: 355.
[16] Jiang Z J. On a class of opertors from weighted Bergman spaces to some spaces of analytic functions [J]. Taiwan J Math, 2011, 15: 2095.
[17] Jiang Z J. Generalized product-type operators from weighted Bergman-Orlicz spaces to Bloch-Orlicz spaces [J]. Appl Math Comput, 2015, 268: 966.
[18] Stevi ?S. Essential norm of some extensions of the generalized composition operators between ?k -th weighted-type spaces [J]. J Inequal Appl, 2017, 220: 1.
[19] Yang W, Yan W. Generalized weighted composition operators from area Nevanlinna spaces to weighted-type spaces [J]. Bull Korean Math Soc, 2011, 48: 1195.
[20] Liu Y M, Yu Y Y. Products of composition, multiplication and radial derivative operators from logarithmic Bloch spaces to weighted-type spaces on the unit ball [J]. J Math Anal Appl, 2015, 423: 76.
[21] Jiang Z J, Wang X F. Products of radial derivative and weighted composition operators from weighted Bergman-Orlicz spaces to weighted-type spaces [J]. Oper Matrices, 2018, 12: 301.
[22] Wang S M, Wang M F, Guo X. Products of composition, multiplication and radial derivative operators between Banach spaces of holomorphic functions on the unit ball [J]. Complex Var Elliptic, 2020, 65: 2026.
[23] Stevi ?S. On some integral-type operators between a general space and Bloch-type spaces [J]. Appl Math Comput, 2011, 218: 2600.
[24] Zhu X. On an integral-type operator from Privalov spaces to Bloch-type spaces [J]. Ann Polon Math, 2011, 101: 139.
[25] Stevi ?S. Weighted iterated radial composition operators between some spaces of holomorphic functions on the unit ball [J]. Abstr Appl Anal, 2010, 2010: 801264.
[26] Stevi ?S, Jiang Z J. Weighted iterated radial composition operators from weighted Bergman-Orlicz spaces to weighted-type spaces on the unit ball [J]. Math Meth Appl Sci, 2021, 44: 8684.
[27] Stevi ?S, Jiang Z J. Weighted iterated radial composition operators from logarithmic Bloch spaces to weighted-type spaces on the unit ball [J]. Math Meth Appl Sci, 2021, 45: 3083.
[28] Beatrous F, Burbea J. Holomorphic Sobolev spaces on the unit ball [J]. Diss Math, 1989, 276: 1.
[29] Zhu K H. Spaces of holomorphic functions in the unit ball [M]. New York: Springer, 2005.
[30] Avetisyan K. Continuous inclusions and Bergman type operators in ?n -harmonic mixed norm spaces on the poly disc [J]. J Math Anal Appl, 2004, 291: 727.
[31] Stevi ?S. A generalization of a result of Choa on analytic functions with Hadamard gaps [J]. J Korean Math Soc, 2006, 43: 579.
[32] Li S X, Stevi ?S. Weighted differentiation composition operators from the logarithmic Bloch space to the weighted-type space [J]. An Stiint Univ ''Ovidius'' Constanta Ser Mat, 2016, 24: 223.
[33] Schwartz H J. Composition operators on ?H p ?[D]. Toledo: University of Toledo, 1969.
[34] Rudin W. Function theory in the unit ball of ?[M]. New York: Springer Verlag, 1980.
[35] Stevi ?S. Weighted radial operator from the mixed-norm space to the ?n -th weighted-type space on the unit ball [J]. Abstr Appl Math Comput, 2012, 218: 9241.