International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 19, Pages 1193-1213

Bergman spaces of temperature functions on a cylinder

Marcos López-García

Instituto de Matemáticas, Universidad Nacional Autónoma de México, Circuito Exterior Ciudad Universitaria, México 04510, D.F., Mexico

Received 19 April 2002

Copyright © 2003 Marcos López-García. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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)=bβp(ST), where β depends on p and β.