Some Linear Operators on Certainfunction Spaces 

Author  XuLiYan 
Tutor  HuZuoJian 
School  Zhejiang Normal University 
Course  Basic mathematics 
Keywords  Function space Linear operator Boundedness Compactness Schattenp class 
CLC  O177 
Type  Master's thesis 
Year  2009 
Downloads  31 
Quotes  0 
The research is divided into two parts . Weighted Bergman space Zygmund space between generalized Ces ( ? ) Ro operator and the product of the composite operator operator boundedness and compactness characteristics ; Second , Schattenp class Hankel operators in the the harmonic Bergman space characteristics . research focused on the following in mind D is the unit disk in the complex plane C , H (D) of holomorphic functions on D plenary given 0
1, the weighted Bergman space on the definition of D dA (z) is the Lebesgue area measure on D normalized the Zygmund space on the definition of D ( ?) which is well known in the norm   f   =  f ( 0 )   f '( 0 )  sup ( 1   z  ~ 2 )  f ( z )  under ( ?) to be a Banach space . the small Zygmund space on the definition of D ( ? ) for given holomorphic self  map φ on D and g ∈ H (D ) , define the generalized Ces ( ? ) ro operator and composition operator multiplication operator T_gC_φ the generalized Ces ( ? ) ro operator an Extension tool can solve when φ (z) = z when , T_gC_φ is generalized Ces ( ? ) ro operator generalized Ces ( ? ) ro operator is the operator an important content in the field of theoretical research , it some function space on the Gleason problem , and it is with the composite operator and operator semigroups have a close relationship , is expected to be used to study some partial differential equations . generalized Ces ( ? ) ro operator and Composition Operators sub product of the operator is also necessary. research we studied operator sub T_gC_φ the weighted Bergman space and Zygmund ( Zygmund) space between the characteristics of the in the appropriate space on T_gC_φ bounded operator compact operator necessary and sufficient conditions on the type of operator extends the scope of the study to enrich people 's understanding of the operator Ω is R ~~ n ( n ≥ 2 ) in a smooth bounded domain , V is the Lebesgue measure on Ω . L ~ 2 (Ω) is a measurable function f on Ω satisfy collection . defined harmonic Bergman Space L_h ~ 2 (Ω) L ~ 2 (Ω) in all harmonic function given f ∈ L to 2 (Ω), define the multiplication operator the sub  M_f M_f ( g ) = fg Let Q L ~ 2 (Ω) to to L_h to 2 ( Ω ) orthogonal projection on the f  symbol L to 2 ( Ω ) on the Hankel operator J_f definition we discuss the Schattenp Hankel operator in L_h ~ 2 (Ω) characteristics obtained when 2 ≤ p <∞ , H_f belong S_p necessary and sufficient conditions , promotion of this there have been results .