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...