经典傅里叶分析

书籍目录

《经典傅里叶分析(第2版)(英文版)》

lp spaces and interpolation

1.1 lp and weak lp

1.2 convolution and approximate identifies

1.3 interpolation

1.4 lorentz spaces

2 maximal functions, fourier transform, and distributions

2.1 maximal functions

2.2 the schwartz class and the fourier transform

2.3 the class of tempered distributions

2.4 more about distributions and the fourier transform

2.5 convolution operators on lp spaces and multipliers

2.6 oscillatory integrals

3 fourier analysis on the torus

3.1 fourier coefficients

3.2 decay of fourier coefficients

3.3 pointwise convergence of fourier series

3.4 divergence of fourier and bochner-riesz summability

3.5 the conjugate function and convergence in norm

3.6 multipliers, transference, and almost everywhere convergence

.3.7 lacunary series

4 singular integrals of convolution type

4.1 the hilbert transform and the riesz transforms

4.2 homogeneous singular integrals and the method of rotations.

4.3 the calder6n-zygmund decomposition and singular integrals

4.4 sufficient conditions for/f boundedness

4.5 vector-valued inequalities

4.6 vector-valued singular integrals

5 littlewood-paley theory and multipliers

5.1 littlewood-paley theory

5.2 two multiplier theorems

5.3 applications of littlewood-paley theory

5.4 the haar system, conditional expectation, and martingales

5.5 the spherical maximal function

5.6 wavelets

a gamma and beta functions

a.1 a useful formula

a.2 definitions off(z) and b(z,w)

a.3 volume of the unit ball and surface of the unit sphere

a.4 computation of integrals using gamma functions

a.5 meromorphic extensions of b(z, w) and f(z)

a.6 asymptotics ofγ(x) as x →∞.

a.7 euler's limit formula for the gamma function

a.8 reflection and duplication formulas for the gamma function

b bessel functions

b.1 definition

b.2 some basic properties

b.3 an interesting identity

b.4 the fourier transform of surface measure on sn-1

b.5 the fourier transform of a radial function on rn

b.6 bessel functions of small arguments

b.7 bessel functions of large arguments

b.8 asymptotics of bessel functions

c rademacher functions

c.1 definition of the rademacher functions

c.2 khintchine's inequalities

c.3 derivation of khintchine's inequalities

c.4 khintchine's inequalities for weak type spaces

c.5 extension to several variables

d spherical coordinates

d.1 spherical coordinate formula

d.2 a useful change of variables formula

d.3 computation of an integral over the sphere

d.4 the computation of another integral over the sphere

d.5 integration over a general surface

d.6 the stereographic projection

e some trigonometric identities and inequalities

f summation by parts

g basic functional analysis

h the minimax lemma

the schur lemma

1.1 the classical schur lemma

1.2 schur's lenuna for positive operators

1.3 an example

j the whitney decomposition of open sets in rn

k smoothness and vauinhing moments

k.1 the case of no cancellation

k.2 the case of cancellation

k.3 the case of three factors

glossary

references

index

作者简介

数学

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