Harmonic analysis

Author: Stan
Publisher:
Publish Date: 2006-01-01
Features: This is one of the most famous and important works in modern analysis mathematics in recent years. Over the past 30 years, harmonic analysis has undergone tremendous development, giving rise to many new results. The main purpose of this book is to provide a comprehensive, systematic, and in-depth exposition of the new developments in this field. The book primarily discusses the following aspects: the real-variable characterization of classical harmonic analysis theory; pseudo-differential operators and singular integral operators; almost orthogonality theory; oscillatory integral theory; maximal operators and maximal averaging theory on Heisenberg groups, and more. The author strives to use hand material and does his best to convey the superiority of each proof method to the readers. The appendices at the end of each chapter provide a detailed review of new research findings and their applications in other disciplines. In summary, this is an exceptional academic monograph that is rigorous in argumentation, rich in content, and profound in depth. This is one of the most famous and important works in modern analysis mathematics in recent years. Over the past 30 years, harmonic analysis has undergone tremendous development, giving rise to many new results, and the main purpose of this book is to provide a comprehensive, systematic, and in-depth exposition of the new developments in this field. The book primarily discusses the following aspects: the real-variable characterization of classical harmonic analysis theory; pseudo-differential operators and singular integral operators; almost orthogonality theory; oscillatory integral theory; maximal operators and maximal averaging theory on Heisenberg groups, and more. The author strives to use hand material and does his best to convey the superiority of each proof method to the readers. The appendices at the end of each chapter provide a detailed review of new research findings and their applications in other disciplines. In summary, this is an exceptional academic monograph that is rigorous in argumentation, rich in content, and profound in depth.