Aspects of Bounded Integral Operators in L^p Spaces

Contents......Page all_23687_to_00529.cpc0004.djvu
Preface......Page all_23687_to_00529.cpc0002.djvu
1.1 Normed linear spaces......Page all_23687_to_00529.cpc0008.djvu
1.2 Examples of Banach spaces......Page all_23687_to_00529.cpc0010.djvu
1.3 Topology in normed linear spaces......Page all_23687_to_00529.cpc0016.djvu
1.4 Separable normed linear spaces......Page all_23687_to_00529.cpc0019.djvu
1.5 Compact sets: the Heine-Borel theorem......Page all_23687_to_00529.cpc0020.djvu
1.6 Baire's category theorem......Page all_23687_to_00529.cpc0022.djvu
1.7 Continuous mappings between normed linear spaces......Page all_23687_to_00529.cpc0023.djvu
1.8 Banach's fixed point theorem......Page all_23687_to_00529.cpc0029.djvu
1.9 Linear transformations in normed linear spaces......Page all_23687_to_00529.cpc0030.djvu
1.10 Extensions of linear mappings: the Hanh-Banach theorem......Page all_23687_to_00529.cpc0036.djvu
1.11 Adjoint mappings......Page all_23687_to_00529.cpc0040.djvu
1.12 Banach algebras......Page all_23687_to_00529.cpc0044.djvu
1.13 Inner product spaces and Hilbert spaces......Page all_23687_to_00529.cpc0051.djvu
1.14 Exercises to Chapter 1......Page all_23687_to_00529.cpc0065.djvu
2.1 Measures and measure spaces......Page all_23687_to_00529.cpc0076.djvu
2.2 Properties of outer measures, and the Lebesgue measure......Page all_23687_to_00529.cpc0078.djvu
2.3 Limit theorems for measures and outer measures......Page all_23687_to_00529.cpc0084.djvu
2.4 Measurable functions......Page all_23687_to_00529.cpc0086.djvu
2.5 Simple functions......Page all_23687_to_00529.cpc0091.djvu
2.6 Convergence theorems......Page all_23687_to_00529.cpc0093.djvu
2.7 The Lebesgue integral of simple functions......Page all_23687_to_00529.cpc0095.djvu
2.8 The Lebesgue integral of a bounded measurable function.......Page all_23687_to_00529.cpc0097.djvu
2.9 The Riemann and Lebesgue integrals on R^1......Page all_23687_to_00529.cpc0105.djvu
2.10 The bounded convergence theorem......Page all_23687_to_00529.cpc0107.djvu
2.11 Integrable functions......Page all_23687_to_00529.cpc0109.djvu
2.12 Distribution functions......Page all_23687_to_00529.cpc0111.djvu
2.13 Convergence theorems......Page all_23687_to_00529.cpc0113.djvu
2.14 Product spaces, product measures: Fubini's theorem......Page all_23687_to_00529.cpc0116.djvu
2.15 Radon-Nikodym theorem: change of variables, derivatives......Page all_23687_to_00529.cpc0122.djvu
2.16 Derivatives and integrals on the real line......Page all_23687_to_00529.cpc0132.djvu
2.17 Appendix to Chapter 2: change of variables in integrals over R^n......Page all_23687_to_00529.cpc0140.djvu
2.18 Exercises to Chapter 2......Page all_23687_to_00529.cpc0145.djvu
3.1 Introduction......Page all_23687_to_00529.cpc0159.djvu
3.2 Holder's inequality......Page all_23687_to_00529.cpc0160.djvu
3.3 Minkowski's inequality and Jensen's inequality......Page all_23687_to_00529.cpc0164.djvu
3.4 Completeness of L^p (X, \textcal{X}, m), p \geq 1 trigonometric series......Page all_23687_to_00529.cpc0168.djvu
3.5 Approximations in L^p(X)......Page all_23687_to_00529.cpc0170.djvu
3.6 Continuity of norm in L^p(R^n)......Page all_23687_to_00529.cpc0175.djvu
3.7 Representation of linear functionais in L^p(X): the adjoint operator......Page all_23687_to_00529.cpc0177.djvu
3.8 Isometries in L^p(X)......Page all_23687_to_00529.cpc0180.djvu
3.9 The pointwise convergence of classes of bounded operators on L^p(R^n)......Page all_23687_to_00529.cpc0186.djvu
3.10 Exercises to Chapter 3......Page all_23687_to_00529.cpc0189.djvu
4.1 A general inequality: Young's inequality for convolutions......Page all_23687_to_00529.cpc0197.djvu
4.2 Inequalities for homogeneous kernels......Page all_23687_to_00529.cpc0200.djvu
4.3 Convolutions and approximations to the identity......Page all_23687_to_00529.cpc0204.djvu
4.4 Operator approximations......Page all_23687_to_00529.cpc0210.djvu
4.5 Special integral operators......Page all_23687_to_00529.cpc0212.djvu
4.6 Exercises to Chapter 4......Page all_23687_to_00529.cpc0224.djvu
5.1 The Riesz-Thorin convexity theorem and extensions......Page all_23687_to_00529.cpc0237.djvu
5.2 Distributions functions and the Marcinkiewicz-Zygmund interpolation theorem......Page all_23687_to_00529.cpc0241.djvu
5.3 An extension of Young's inequality for generalized convolution......Page all_23687_to_00529.cpc0252.djvu
5.4 Non-increasing rearrangements......Page all_23687_to_00529.cpc0255.djvu
5.5 Lorentz spaces......Page all_23687_to_00529.cpc0261.djvu
5.6 Further results involving convolutions......Page all_23687_to_00529.cpc0265.djvu
5.7 Maximal functions......Page all_23687_to_00529.cpc0271.djvu
5.8 Weighted norms for operators mapping into L^\infty......Page all_23687_to_00529.cpc0279.djvu
5.9 Exercises to Chapter 5......Page all_23687_to_00529.cpc0281.djvu
6.1 Fourier transforms of functions in L^1(R^n)......Page all_23687_to_00529.cpc0299.djvu
6.2 Some special theorems: special functions and radial functions......Page all_23687_to_00529.cpc0303.djvu
6.3 Fourier transforms of functions in L^2(R^n)......Page all_23687_to_00529.cpc0311.djvu
6.4 Fourier transforms in L^p(R^n), 1 \geq p \geq 2......Page all_23687_to_00529.cpc0317.djvu
6.5 Fourier transforms with weight functions......Page all_23687_to_00529.cpc0320.djvu
6.6 Fourier transforms, fractional integrals and Bessel potentials......Page all_23687_to_00529.cpc0337.djvu
6.7 Operators with Fourier-type kernels: generalized transforms......Page all_23687_to_00529.cpc0341.djvu
6.8 Laplace transforms and Mellin transforms......Page all_23687_to_00529.cpc0351.djvu
6.9 Exercises to Chapter 6......Page all_23687_to_00529.cpc0355.djvu
7.1 Introduction to the Hilbert transform......Page all_23687_to_00529.cpc0368.djvu
7.2 The Hilbert transform in L^2(R)......Page all_23687_to_00529.cpc0372.djvu
7.3 Hilbert transforms and conjugate functions in L^p(R)......Page all_23687_to_00529.cpc0378.djvu
7.4 Fourier transform multipliers: Dirichlet projections......Page all_23687_to_00529.cpc0393.djvu
7.5 Estimates for singular integrals: An estimate for differentiable multipliers......Page all_23687_to_00529.cpc0407.djvu
7.6 Maximal functions for convolution operators......Page all_23687_to_00529.cpc0429.djvu
7.7 Exercises to Chapter 7......Page all_23687_to_00529.cpc0436.djvu
8.2 Equivalent functional relations: translation invariant operators......Page all_23687_to_00529.cpc0444.djvu
8.3 Vector-valued functions on measure spaces......Page all_23687_to_00529.cpc0451.djvu
8.4 Estimates for vector-valued singular integrals......Page all_23687_to_00529.cpc0462.djvu
8.5 Mixed-norm estimates for singular integrals......Page all_23687_to_00529.cpc0464.djvu
8.6 Semi-groups of operators......Page all_23687_to_00529.cpc0474.djvu
8.7 Examples of special semi-groups of operators on L^p(R^n)......Page all_23687_to_00529.cpc0490.djvu
8.8 Remarks on semi-group potential theory......Page all_23687_to_00529.cpc0494.djvu
8.9 Exercises to Chapter 8......Page all_23687_to_00529.cpc0495.djvu
Notation not defined in Text......Page all_23687_to_00529.cpc0509.djvu
Bibliography and References......Page all_23687_to_00529.cpc0511.djvu
Author Index......Page all_23687_to_00529.cpc0518.djvu
Subject Index......Page all_23687_to_00529.cpc0521.djvu