On subspaces of Bloch space and series with Hadamard gaps. (English) Zbl 1054.30527
Summary: In this paper, we study a collection of subclasses of Bloch spaces defined by means of a modified Besov norm and show that these classes are equivalently defined by means of a modified Carleson measure. We use the relations between these classes and series with Hadamard gaps to imply the proper inclusion among these classes. Finally, as a simple consequence of our results, we give a negative answer to an open problem raised by K. Stroethoff on BMOA and VMOA.
MSC:
| 30D50 | Blaschke products, etc. (MSC2000) |
| 30B10 | Power series (including lacunary series) in one complex variable |
| 30D45 | Normal functions of one complex variable, normal families |
| 46E10 | Topological linear spaces of continuous, differentiable or analytic functions |
