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The Blocking Technique, Weighted Mean Operators and Hardy's Inequality
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This book presents the first comprehensive treatment of the blocking technique which consists in transforming norms in section form into norms in block form, and vice versa. Such norms appear throughout analysis. The blocking technique is a powerful, yet elementary, tool whose usefulnes is demonstrated in the book. In particular, it is shown to lead to the solution of three recent problems of Bennett concerning the inequalities of Hardy and Copson. The book is addressed to researchers and graduate students. An interesting feature is that it contains a dictionary of transformations between section and block norms and will thus be useful to researchers as a reference text. The book requires no knowledge beyond an introductory course in functional analysis. TOC:Introduction.- The Blocking Technique.- The Sequence Spaces c(a,p,q) and d(a,p,q).- Applications to matrix operators and inequalities.- Integral analogues.- Appendix. Equivalence of section conditions with block conditions.- References.- Index.
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