Distance of a Bloch Function to the Little Bloch Space
نویسندگان
چکیده
منابع مشابه
Singular Measures and the Little Bloch Space
Aleksandrov, Anderson and Nicolau have found examples of inner functions that are in the little Bloch space with a specific rate of convergence to zero. As a corollary they obtain positive singular measures defined in the boundary of the unit disc that are simoultaneously symmetric and Kahane. Nevertheless their construction is very indirect. We give an explicit example of such measures by mean...
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CHRISTOPHER J . BISHOP The little Bloch space, 130 , is the space of all holomorphic functions f on the unit disk such that lim1 z 1l (f'(z)j(1 Iz12) = 0. Finite Blaschke products are clearly in 130, but examples of infinite products in 80 are more difficult to obtain (there are now several constructions due to Sarason, Stephenson and the author, among others) . Stephenson has asked whether 130...
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Let ϕ(z) = (ϕ 1 (z),...,ϕ n (z)) be a holomorphic self-map of D n and ψ(z) a holomorphic function on D n , where D n is the unit polydiscs of C n. Let 0 < α, β < 1, we compute the essential norm of a weighted composition operator ψC ϕ between α-Bloch space Ꮾ α (D n) and β-Bloch space Ꮾ β (D n).
متن کاملInner Functions in the Hyperbolic Little Bloch Class
An analytic function φ mapping the unit disk into itself is said to belong to the hyperbolic little Bloch class if the ratio (1−|z|2)|φ′(z)|/(1−|φ(z)|2) converges to 0 as |z| → 1, while φ is in the little Bloch space if just the numerator of this expression converges to zero. Several constructions of inner functions in the little Bloch space have recently appeared. In this paper we construct a ...
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ژورنال
عنوان ژورنال: Bulletin of the Australian Mathematical Society
سال: 2006
ISSN: 0004-9727,1755-1633
DOI: 10.1017/s0004972700047493