International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 19, Pages 1193-1213
doi:10.1155/S0161171203204178

Bergman spaces of temperature functions on a cylinder

Abstract

We define the weighted Bergman space bβp(ST) consisting of temperature functions on the cylinder ST=S1×(0,T) and belonging to Lp(ΩT,tβdxdt), where ΩT=(0,2)×(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.