Bloch-type space of temperature functions on a finite cylinder

We define the Bloch-type space BT as the linear space of temperature functions on the cylinder ST=1×(0,T) such that sup⁡(x,t)∈T⁡t|∂u∂t(x,t)|<∞, ΩT=[0,2]×(0,T); we prove that (b1(ST))*=BT, where b1(ST) is the Bergman space of temperature functions on ST belonging to L1(ΩT,dxdt)