Fundamentals of Fourier Analysis

This text serves as an introduction to Fourier Analysis for graduate students. Fundamentals of Fourier Analysis emphasizes clarity, exercises, and detailed proofs.

This comprehensive text serves as an introduction to Fourier Analysis, specifically tailored for graduate students who have a background in Real Analysis and Complex Variables. Fundamentals of Fourier Analysis is designed to be self-contained, making it suitable for a two-course sequence in either Fourier Analysis or Harmonic Analysis at the graduate level. Each chapter is thoughtfully structured, offering a selection of exercises accompanied by targeted hints, which help students develop essential research skills and deepen their understanding of the subject matter.

In Fundamentals of Fourier Analysis, the author emphasizes clarity and precision in the presentation of proofs, ensuring that each step is carefully detailed. To enhance comprehension, the text includes numerous examples that illustrate key concepts, alongside carefully crafted illustrations that foster intuition regarding the proofs. Additionally, appendices provide background material for those who may need to revisit foundational concepts, making the book accessible to a wider audience.

Compared to the author's previous works, such as Classical Fourier Analysis and Modern Fourier Analysis, this text adopts a more classroom-friendly approach. It features shorter sections, more refined proofs, and a broader range of exercises, facilitating a smoother learning experience. Key topics covered include the Fourier Transform, Multipliers, Singular Integrals, Littlewood–Paley Theory, BMO, Hardy Spaces, and Weighted Estimates, all of which can be effectively explored within two semesters.