The book is a summation of the study by the authors on Herz spaces in recent 20 years.

The content of the book mainly includes the following sides: decomposition characterization of homogeneous and non-homogeneous Herz spaces in terms of central blocks, decomposition characterization of homogeneous and non-homogeneous Herz type Hardy spaces in terms of central atoms and molecules, interpolations and duals for Herz type spaces and applications of above decomposition characterizations to boundedness of operators.

Preface

Chapter 1 Herz Spaces

 1.1 Definitions and some basic facts

 1.2 Dual spaces of the Herz spaces

 1.3 Block decompositions for the Herz spaces

 1.4 The weak Herz spaces

 1.5 Notes and related results

Chapter 2 Herz-type Hardy Spaces

 2.1 Definitions and basic properties

 2.2 The atom decompositions

 2.3 The molecular decompositions

 2.4 Weighted Herz type Hardy spaces

 2.5 Embedding theorems for Herz-type Hardy spaces

 2.6 Local Herz-type Hardy spaces

 2.7 Notes and related results

Chapter 3 Characterizations of ф-transforms and Wavelet Transforms

 3.1 The discrete weighted Herz-type tent space

 3.2 The ф-transform characterizations

 3.3 The wavelet characterizations

 3.4 Notes and related results

Chapter 4 Interpolations for Herz Type Spaces

 4.1 Complex interpolation for Herz spaces of Banach type

 4.2 The complex interpolation for Herz spaces of quasi-Banach type

 4.3 Interpolation for families

 4.4 Interpolation for mixed couples

 4.5 Notes and related results..

Chapter 5 Boundedness of Sublinear Operators on Herz Spaces

 5.1 Sublinear operators on Herz spaces

 5.2 Some weak type results

 5.3 Rough operators on Herz spaces

 5.4 g-function and Lusin area function characterization of Herz spaces

 5.5 Notes and related results

Chapter 6 Boundedness of Some Operators on Herz-type Hardy Spaces

 6.1 Operators on Herz-type Hardy space

 6.2 Singular integral operators

 6.3 Oscillatory integral operators on Herz type Hardy spaces

 6.4 Bilinear operators

 6.5 Multiplier for Herz type Hardy spaces

 6.6 Notes and related results

Reference

Appendix A

Appendix B