Harmonic analysis on spaces of homogeneous type / Donggao Deng, Yongsheng Han ; with a preface by Yves Meyer.

Format:

Book

Author/Creator:

Deng, Dong-Gao, 1935-

Contributor:

Han, Yongsheng.

Series:

Lecture notes in mathematics (Springer-Verlag) ; 1966.

Lecture notes in mathematics ; 1966

Language:

English

Subjects (All):

Harmonic analysis.

Spaces of homogeneous type.

Physical Description:

xii, 154 pages ; 24 cm.

Place of Publication:

Berlin : Springer, [2009]

Summary:

The dramatic changes that came about in analysis during the twentieth century are truly amazing. In the thirties, complex methods and Fourier series played a seminal role. After many improvements, mostly achieved by the Calderon-Zygmund school, the action today is taking place in spaces of homogeneous type. No group structure is available and the Fourier transform is missing, but a version of harmonic analysis is still available. Indeed the geometry is conducting the analysis. The authors succeed in generalizing the construction of wavelet bases to spaces of homogeneous type. However wavelet bases are replaced by frames, which in many applications serve the same purpose.

Contents:

1 Calderon-Zygmund Operator on Space of Homogeneous Type 9

1.2 Definition of Calderon-Zygmund Operators on Spaces of Homogeneous Type 9

1.3 Littlewood-Paley Analysis on Spaces of Homogeneous Type 15

1.4 The T1 Theorem on Spaces of Homogeneous Type 19

2 The Boundedness of Calderon-Zygmund Operators on Wavelet Spaces 27

3 Wavelet Expansions on Spaces of Homogeneous Type 39

3.2 The Theory of Frames 41

3.3 Approximation to the Identity and Basic Estimates 43

3.4 Calderon's Identity on Spaces of Homogeneous Type 52

3.5 Wavelet Expansions on Spaces of Homogeneous Type 73

4 Wavelets and Spaces of Functions and Distributions 91

4.2 Comparison Properties of Wavelet Coefficients 92

4.3 Holder Spaces 97

4.4 Lebesgue and Generalized Sobolev Spaces 101

4.5 Wavelets, the Hardy and BMO Spaces 105

4.6 Besov Spaces on Spaces of Homogeneous Type 115

4.7 The T1 Type Theorems 116

5 Littlewood-Paley Analysis on Non Homogeneous Spaces 137

5.2 Littlewood-Paley Theory on Non Homogeneous Spaces 139

5.3 The T1 Theorem on Non Homogeneous Spaces 143

5.4 The Besov Space on Non Homogeneous Spaces 145.

Notes:

Includes bibliographical references and index.

ISBN:

9783540887447

354088744X

3540887458

9783540887454

OCLC:

262720652