and Applied Analysis 3 2. Main Results and Proofs In this section, we give our main results and their proofs. Before stating these results, we need some auxiliary results, which are incorporated in the lemmas which follows. Lemma 2.1. Assume that g ∈ H Bn and μ : Bn → 0,∞ are normal. Then Tg : H∞ log → Bμ is compact if and only if Tg : H∞ log → Bμ is bounded and for any bounded sequence fk k∈N ...