Volterra Type Operators from Bergman Spaces with Exponential Weights to the Bloch Space

We study the asymptotic behaviour of the powers of a composition operator on various Banach spaces of holomorphic functions on the disc, namely, standard weighted Bergman spaces (finite and infinite order), Bloch space, little Bloch space, Bloch-type space and Dirichlet space. Moreover, we give a complete characterization of those composition operators that are similar to an isometry on these various Banach spaces. We conclude by studying the asymptotic behaviour of semigroups of composition operators on these various Banach spaces.

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Multiplicative Isometries and Isometric Zero-Divisors

Canadian Journal of Mathematics ◽

10.4153/cjm-2010-048-7 ◽

2010 ◽

Vol 62 (5) ◽

pp. 961-974 ◽

Cited By ~ 10

Author(s):

Alexandru Aleman ◽

Peter Duren ◽

María J. Martín ◽

Dragan Vukotić

Keyword(s):

Banach Spaces ◽

Bloch Space ◽

Bergman Spaces ◽

Weighted Bergman Spaces ◽

Zero Divisors ◽

Pointwise Multipliers ◽

Type Spaces ◽

Dirichlet Type Spaces ◽

Coefficient Multipliers ◽

Spaces Of Analytic Functions

AbstractFor some Banach spaces of analytic functions in the unit disk (weighted Bergman spaces, Bloch space, Dirichlet-type spaces), the isometric pointwise multipliers are found to be unimodular constants. As a consequence, it is shown that none of those spaces have isometric zero-divisors. Isometric coefficient multipliers are also investigated.

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Characterizations of Bergman Spaces and Bloch Space in the Unit Ball of C n

Transactions of the American Mathematical Society ◽

10.2307/2155039 ◽

1995 ◽

Vol 347 (11) ◽

pp. 4301 ◽

Cited By ~ 13

Author(s):

Caiheng Ouyang ◽

Weisheng Yang ◽

Ruhan Zhao

Keyword(s):

Unit Ball ◽

Bloch Space ◽

Bergman Spaces

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Volterra composition operators from generalized weighted weighted Bergman spaces toµ-Bloch spaces

Journal of Function Spaces and Applications ◽

10.1155/2009/179381 ◽

2009 ◽

Vol 7 (3) ◽

pp. 225-240 ◽

Cited By ~ 1

Author(s):

Xiangling Zhu

Keyword(s):

Holomorphic Function ◽

Unit Ball ◽

Bergman Space ◽

Composition Operators ◽

Bloch Space ◽

Bergman Spaces ◽

Weighted Bergman Space ◽

Weighted Bergman Spaces ◽

Bloch Spaces

Letφbe a holomorphic self-map andgbe a fixed holomorphic function on the unit ballB. The boundedness and compactness of the operatorTg,φf(z)=∫01f(φ(tz))ℜg(tz)dttfrom the generalized weighted Bergman space into the µ-Bloch space are studied in this paper.

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