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 basic 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 cover fields such as function theory, 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 many years of experience teaching the course at the Department of Mathematics, Peking University, and has been supplemented and organized based on the lecture notes used. The book pays special attention to aligning with undergraduate-level content, for which the author has written a dedicated chapter titled "Basic Knowledge," making it easier for readers to learn and improving learning efficiency. Each chapter is equipped with a sufficient number of exercises and a list of references, while the appendix provides solutions and hints for the exercises for reference by teachers and students. This book is suitable as a textbook or teaching reference for senior undergraduate and graduate students in mathematics and related majors in higher education institutions, as well as for mathematics teachers and scientific and technological workers.