单位球上加权Bergman空间到加权型空间上的算子CφRmMu

黄成世 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.