不等式

II10.6 Notes and remarks11 The Hilbert transform, and Hilbert's inequalities11.1 The conjugate Poisson kernel11.2 The Hilbert transform on11.3 The Hilbert transform on11.4 Hilbert's inequality for sequences11.5 The Hilbert transform on T11.6 Multipliers11.7 Singular integral operators11.8 Singular integral operators on11.9 Notes and remarks12 Khintchine's inequality12.1 The contraction principle12.2 The reflection principle, and Lavy's inequalities12.3 Khintchine's inequality12.4 The law of the iterated logarithm12.5 Strongly embedded subspaces12.6 Stable random variables12.7 Sub-Gaussian random variables12.8 Kahane's theorem and Kahane's inequality12.9 Notes and remarks13 Hypercontractive and logarithmic Sobolev inequalities13.1 Bonami's inequality13.2 Kahane's inequality revisited13.3 The theorem of Lataa and Oleszkiewicz13.4 The logarithmic Sobolev inequality on Dd13.5 Gaussian measure and the Hermite polynomials13.6 The central limit theorem13.7 The Gaussian hypercontractive inequality13.8 Correlated Gaussian random variables13.9 The Gaussian logarithmic Sobolev inequality13.10 The logarithmic Sobolev inequality in higher dimensions13.11 Beckner's inequality13.12 The Babenko-Beckner inequality13.13 Notes and remarks14 Hadamard's inequality14.1 Hadamard's inequality14.2 Hadamard numbers14.3 Error-correcting codes14.4 Note and remark15 Hilbert space operator inequalities15.1 Jordan normal form15.2 Riesz operators15.3 Related operators15.4 Compact operators15.5 Positive compact operators15.6 Compact operators between Hilbert spaces15.7 Singular numbers, and the Rayleigh-Ritz minimax formula15.8 Weyl's inequality and Horn's inequality15.9 Ky Fan's inequality15.10 Operator ideals15.11 The Hilbert-Schmidt class15.12 The trace class15.13 Lidskii's trace formula15.14 Operator ideal duality15.15 Notes and remarks16 Summing operators16.1 Unconditional convergence16.2 Absolutely summing operators16.3 (p, q)-summing operators16.4 Examples of p-summing operators16.5 (p, 2)-summing operators between Hilbert spaces16.6 Positive operators on16.7 Mercer's theorem16.8 p-summing operators between Hilbert spaces16.9 Pietsch's domination theorem16.10 Pietsch's factorization theorem16.11 p-summing operators between Hilbert spaces16.12 The Dvoretzky-Rogers theorem16.13 Operators that factor through a Hilbert space16.14 Notes and remarks17 Approximation numbers and eigenvalues17.1 The approximation, Gelfand and Weyl numbers17.2 Subadditive and submultiplicative properties17.3 Pietsch's inequality17.4 Eigenvalues of p-summing and (p, 2)-summingendomorphisms17.5 Notes and remarks18 Grothendieck's inequality, type and cotype18.1 Littlewood's 4/3 inequality18.2 Grothendieck's inequality18.3 Grothendieck's theorem18.4 Another proof, using Paley's inequality18.5 The little Grothendieck theorem18.6 Type and cotype18.7 Gaussian type and cotype18.8 Type and cotype of LP spaces18.9 The little Grothendieck theorem revisited18.10 More on cotype18.11 Notes and remarksReferencesIndex of inequalitiesIndex

　　本书旨在介绍大量运用于线性分析中的不等式，并且详细介绍它们的具体应用。本书以柯西不等式开头，grothendieck不等式结束，中间用许多不等式串成一个完整的篇幅，如，loomiswhitney不等式、最大值不等式、hardy和hilbert不等式、超收缩和拉格朗日索伯列夫不等、beckner以及等等。这些不等式可以用来研究函数空间的性质，它们之间的线性算子，以及绝对和算子。书中拥有许多完整和标准的结果，提供了许多应用，如勒贝格分解定理和勒贝格密度定理、希尔伯特变换和其他奇异积分算子、鞅收敛定理、特征值分布、lidskii积公式、mercer定理和littlewood4/3定理。本书由(英)加林著。