Logarithmic Bloch Space and Its Predual
نویسنده
چکیده
We consider the space B logα , of analytic functions on the unit disk D, defined by the requirement ∫ D |f (z)|φ(|z|) dA(z) < ∞, where φ(r) = log(1/(1 − r)) and show that it is a predual of the “log-Bloch” space and the dual of the corresponding little Bloch space. We prove that a function f(z) = ∑ ∞ n=0 anz with an ↓ 0 is in B1logα iff ∑ ∞ n=0 log(n+2)/(n+1) < ∞ and apply this to obtain a criterion for membership of the Libera transform of a function with positive coefficients in B logα . Some properties of the Cesàro and the Libera operator are considered as well.
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