This book introduces some important progress in the theory of Calderon–Zygmund singular integrals, oscillatory singular integrals, and Littlewood–Paley theory over the last decade. It includes some important research results by the authors and their cooperators, such as singular integrals with rough kernels on Block spaces and Hardy spaces, the criterion on boundedness of oscillatory singular integrals, and boundedness of the rough Marcinkiewicz integrals. These results have frequently been cited in many published papers.

Contents:

• Hardy–Littlewood Maxial Operator
• Singular Integral Operators
• Fractional Integral Operators
• Oscillatory Singular Integrals
• Littlewood–Paley Operator

“All the results in the book are written in the context of Euclidean spaces and they are very clearly presented. Many of the results in the last three chapters of the book reflect several advancements in the theory made by the Beijing harmonic analysis school of Professor Shanzhen Lu. This book provides excellent background material for further research in the topics that it covers in the last three chapters.”

“… they aim to establish a more perfect theory of singular integrals with rough kernels. For graduate students in analysis, this book is a nice introduction to the theory.”