It is well known that the study on Hp spaces has been going on for along period. The classical Hp spaces on the unit circle or upper half-plane are defined by the aid of complex method. The theory of these spaces plays an important role in the study of the classical Fourier analysis. It is natural to extend the definitions of these spaces to higher dimensional case along with the development of the Fourier analysis on Euclidean spaces.

Preface

Chapter 1 Real Variable Theory of HPSpaces

 1 Definition of HP spaces

 2 Non-tangential maximal functions

 3 Grand maximal functions

Chapter 2 Decomposition Structure Theory of HP Spaces

 1 Atom

 2 Dual space of HI

 3 Atom decomposition

 4 Dual space of HP

 5 Interpolation of operators

 6 Interpolations of HP spaces; weak Hp spaces

 7 Molecule; molecule decomposition

 8 Applications to the boundedness of operators

Chapter 3 Applications to Fourier Analysis

 1 Fourier transform

 2 The Fourier multiplier

 3 The Riesz potential operators

 4 Singular integral operators

 5 The Bochner-Riesz means

 6 Transference theorems of Hp multipliers

Chpater 4 Applications to Approximation Theory

 1 K functional

 2 Hp multiplier and Jackson-type inequality

 3 Hp multiplier and Bernstein type inequality

 4 Approximation by Bochner-Riesz means at critical index

References