Some Linear Operators on Certainfunction Spaces
|School||Zhejiang Normal University|
|Keywords||Function space Linear operator Boundedness Compactness Schatten-p class|
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 , Schatten-p 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 Schatten-p 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 .