Harmonic Analysis Lectures (Real Analysis Methods)

Author: Zhou Minqiang
Publisher:
Publish Date: 2003-06-01
Features: This book is a textbook for mathematics, applied mathematics, and related majors in higher education institutions, focusing on systematically introducing the fundamental theories and methods of modern harmonic analysis using measure-theoretic methods. The book is divided into eight chapters. The content includes: maximal functions, operator interpolation theory, function space decomposition, singular integral operators, weighted modulus inequalities, and bounded mean oscillation function spaces, among others. Its applications span fields such as functional analysis, partial differential equations, and probability theory.
Harmonic Analysis has long been offered as a graduate-level course in universities, but there are few teaching textbooks published domestically. This book summarizes the author's years of experience teaching the course at the Department of Mathematics, Peking University, and is based on the lecture notes supplemented and personally organized. The book pays special attention to aligning with undergraduate-level content, for which the author has written a dedicated chapter titled "Foundations." This not only facilitates learning but also enhances efficiency. Each chapter includes a selection of exercises and references, while the appendix provides solutions and hints for teachers and students to consult.
This book is suitable as a textbook or teaching reference for senior undergraduate and graduate students in mathematics and related fields at higher education institutions, as well as for mathematics teachers and scientific researchers.