in this paper boundedness and compactness of generalized composition oper-ators from logarithmic bloch type spaces to q_k type spaces are investigated.

In this paper boundedness and compactness of generalized composition oper-ators from logarithmic Bloch type spaces to Q_K type spaces are investigated.

Recommended by Radu Precup The boundedness and compactness of the weighted composition operators from logarithmic Bloch-type spaces to Bloch-type spaces are studied here.

We prove, for an arithmetic scheme X/S over a discrete valuation ring whose special fiber is a strict normal crossings divisor in X, that the Swan conductor of X/S is equal to the Euler characteristic of the torsion in the logarithmic de Rham complex of X/S. This is a precise logarithmic analog of a theorem by Bloch [1].

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 crit...