Bergman spaces of temperature functions on a cylinder

We define the weighted Bergman space bβp (ST) consisting of temperature functions on the cylinder ST=S1x (0,T) and belonging to Lp (ΩT,tβdxdt), where ΩT= (0,2)x (0,T). For β>-1 we construct a family of bounded projections of Lp (ΩT,tβdxdt) onto bβp (ST). We use this to get, for 1<p<∞ and 1/p+ 1/ p′=1, a duality bβp (ST)□=bβ′p′ (ST), where β′ depends on p and β.