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 = S-1 x (0,T) such that sup t sup t | partial derivative u/partial derivative t(x, t) | < infinity, Omega(T) = [0, 2] x (0, T); we prove that (b(1) (S-T))* = B-T, (x, t) epsilon Omega(T) where b(1)(S-T) is the Bergman space of temperature functions on S-T belonging to L-1 (Omega(T), dxdt).