Finite Sections of Some Classical Inequalities

Hardy, Littlewood and P6lya's famous monograph on inequalities [17J has served as an introduction to hard analysis for many mathema­ ticians. Some of its most interesting results center around Hilbert's inequality and generalizations. This family of inequalities determines the best bound of a family of operators on /p. When such inequalities are restricted only to finitely many variables, we can then ask for the rate at which the bounds of the restrictions approach the uniform bound. In the cont