LOGARITHMIC BLOCH SPACE AND ITS PREDUAL.

We consider the space of analytic functions on the unit disk D, defined by the requirement fD f′(z) ø(z) dA(z) < ∞, where ø(r) = logα(1/(1 - r)) and show that it is a predual of the "logα-Bloch" space and the dual of the corresponding little Bloch space. We prove that a function with an ↓ 0 is in iffP∞ logα(n+2)/(n+1) < ∞ and apply this to obtain a criterion for membership of the Libera transform of a function with positive coefficients in Some properties of the Cesàro and the Libera operator are considered as well. [ABSTRACT FROM AUTHOR]