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内容简介

Thus there are very many important inequalities.This book is not intended to be a compendium of these; instead， it provides an introduction to a selection of inequalities， not including any of those mentioned above. The inequalities that we consider have a common theme; they relate to problems in real analysis， and more particularly to problems in real analysis. Incidentally， they include many of the inequalities considered in the fascinating and ground-breaking book Inequalities，by Hardy， Littlewood and Polya， originally published in 1934.

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目录

Introduction
1 Measure and integral
1.1 Measure
1.2 Measurable functions
1.3 Integration
1.4 Notes and remarks

2 The Cauchy-Schwarz inequality
2.1 Cauchy's inequality
2.2 Inner-product spaces
2.3 The Cauchy-Schwarz inequality
2.4 Notes and remarks
3 The AM-GM inequality
3.1 The AM-GM inequality
3.2 Applications
3.3 Notes and remarks

4 Convexity and Jensen's inequality
4.1 Convex sets and convex functions
4.2 Convex functions on an interval
4.3 Directional derivatives and sublinear functionals
4.4 The Hahn-Banach theorem
4.5 Normed spaces, Banach spaces and Hilbert space
4.6 The Hahn-Banach theorem for normed spaces
4.7 Barycentres and weak integrals
4.8 Notes and remarks

5 The Lp spaces
5.1 Lp spaces, and Minkowski's inequality
5.2 The Lebesgue decomposition theorem
5.3 The reverse Minkowski inequality
5.4 HSlder's inequality
5.5 The inequalities of Liapounov and Littlewood
5.6 Duality
5.7 The Loomis-Whitney inequali'ty
5.8 A Sobolev inequality
5.9 Schur's theorem and Schur's test
5.10 Hilbert's absolute inequality
5.11 Notes and remarks

6 Banach function spaces
6.1 Banach function spaces
6.2 Function space duality
6.3 Orlicz space
6.4 Notes and remarks

7 Rearrangements
7.1 Decreasing rearrangements
7.2 Rearrangement-invariant Banach function spaces
7.3 Muirhead's maximal function
7.4 Majorization
7.5 Calder6n's interpolation theorem and its converse
7.6 Symmetric Banach sequence spaces
7.7 The method of transference
7.8 Finite doubly stochastic matrices
7.9 Schur convexity
7.10 Notes and remarks Maximal inequalities

8.1 The Hardy-Riesz inequality
8.2 The Hardy-Riesz inequality
8.3 Related inequalities
8.4 Strong type and weak type
8.5 Riesz weak type
8.6 Hardy, Littlewood, and a batsman's averages
8.7 Riesz's sunrise lemma
8.8 Differentiation almost everywhere
8.9 Maximal operators in higher dimensions
8.10 The Lebesgue density theorem
8.11 Convolution kernels
8.12 Hedberg's inequality
……
9 Complex interpolation
10 Real interpolation
11 The Hilbert transform, and Hilbert's inequalities
12 Khintchine's inequality
13 Hypercontractive and logarithmic Sobolev inequalities
14 Hadamard's inequality
15 Hilbert space operator inequalities
16 Summing operators
17 Approximation numbers and eigenvalues
18 Grothendieck's inequality, type and cotype
References
Index of inequalities
Index

前言/序言

不等式（英文） [Inequalities:A Journey into Linear Analysis] 电子书 下载 mobi epub pdf txt

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不等式很重要，好评！

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哈哈，英文原版的，读着比起中译本舒服。

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开卷有益处,不忘送书人

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真的非常喜欢这款商品，真的真的非常喜欢！！！

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以后准备做分析，买来参考

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帮朋友买的，不知道够不够格作为Hardy书的继承和延续者

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5 Algebraic Curves and Riemann Surfaces, Rick Miranda (1995, ISBN

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还 不 错

评分☆☆☆☆☆

哈哈，英文原版的，读着比起中译本舒服。

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