New estimates of essential norm of an integral-type operator 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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and Applied Analysis 3 The weighted-type space H∞ μ B H ∞ μ 2, 3 consists of all f ∈ H B such that ‖f‖H∞ μ : sup z∈B μ z ∣ ∣f z ∣ ∣ < ∞, 1.11 where μ is a positive continuous function on B weight . The Bloch-type space Bμ B Bμ consists of all f ∈ H B such that ‖f‖Bμ : ∣ ∣f 0 ∣ ∣ sup z∈B μ z ∣ ∣Rf z ∣ ∣ < ∞, 1.12 where μ is a weight. Let g ∈ H D , g 0 0, and φ be a holomorphic self-map of B, the...
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ژورنال
عنوان ژورنال: Mathematical Inequalities & Applications
سال: 2016
ISSN: 1331-4343
DOI: 10.7153/mia-19-20