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Composition operators: $N_α$ to the Bloch space to $Q_β$

100%

Xiao J.

Studia Mathematica

2000

tom 139

nr 3

245-260

Let $N_α$,B and Q_β be the weighted Nevanlinna space, the Bloch space and the Q space, respectively. Note that B and $Q_β$ are Möbius invariant, but $N_α$ is not. We characterize, in function-theoretic terms, when the composition operator $C_ϕ f=f◦ϕ$ induced by an analytic self-map ϕ of the unit disk defines an operator $C_ϕ:N_α→B$, $B→Q_β$, $N_α→Q_β$ which is bounded resp. compact.

Reducing subspaces for multiplication operators on the Dirichlet space through local inverses and Riemann surfaces

51%

Gu C., Luo S., Xiao J.

Complex Manifolds

2017

tom 4

nr 1

84-119

This paper gives a full characterization of the reducing subspaces for the multiplication operator Mϕ on the Dirichlet space with symbol of finite Blaschke product ϕ of order 5I 6I 7. The reducing subspaces of Mϕ on the Dirichlet space and Bergman space are related. Our strategy is to use local inverses and Riemann surfaces to study the reducing subspaces of Mϕ on the Bergman space. By this means, we determine the reducing subspaces of Mϕ on the Dirichlet space and answer some questions of Douglas-Putinar-Wang in [6].

Ograniczanie wyników

1 Complex Manifolds

1 Studia Mathematica

2 Xiao J.

1 Gu C.

1 Luo S.

1 2017

1 2000

Wyniki wyszukiwania

Composition operators: $N_α$ to the Bloch space to $Q_β$

Reducing subspaces for multiplication operators on the Dirichlet space through local inverses and Riemann surfaces