On an Integral-Type Operator Acting between Bloch-Type Spaces on the Unit Ball
نویسندگان
چکیده
منابع مشابه
On an Integral-Type Operator Acting between Bloch-Type Spaces on the Unit Ball
and Applied Analysis 3 Here H∞ ω denotes the weighted-type space consisting of all f ∈ H B with ∥ ∥f ∥ ∥ H∞ ω sup z∈B ω z ∣ ∣f z ∣ ∣ < ∞ 1.9 see, e.g., 23, 24 . Associated weights assist us in studying of weighted-type spaces of holomorphic functions. It is known that associated weights are also continuous, 0 < ω ≤ ω̃, and for each z ∈ B, we can find an fz ∈ H∞ ω , ‖fz‖H∞ ω ≤ 1 such that fz z 1/...
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Let H(B) denote the space of all holomorphic functions on the unit ball B of Cn . Let α > 0 , f ∈ H(B) with homogeneous expansion f = ∑k=0 fk . The fractional derivative Dα f is defined as Dα f (z) = ∞ ∑ k=0 (k+1)α fk(z). Let φ be a holomorphic self-map of B and g ∈ H(B) such that g(0) = 0 . In this paper we consider the following integral-type operator
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Let H(B) be the space of all holomorphic functions on the unit ball B in CN , and S(B) the collection of all holomorphic self-maps of B . Let φ ∈ S(B) and g ∈ H(B) with g(0) = 0 , the generalized composition operator is defined by C φ ( f )(z) = ∫ 1 0 R f (φ(tz))g(tz) dt t , Here, we characterize the boundedness and compactness of the generalized composition operator acting from Bloch-type spac...
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ژورنال
عنوان ژورنال: Abstract and Applied Analysis
سال: 2010
ISSN: 1085-3375,1687-0409
DOI: 10.1155/2010/214762