Castillo R.E. Fourier Meets Hilbert and Riesz - An Introduction to the Corresponding Transforms

Berlin: de Gruyter, 2022. — 307 p.This book provides an introduction into the modern theory of classical harmonic analysis, dealing with Fourier analysis and the most elementary singular integral operators, the Hilbert transform and Riesz transforms. Ideal for self-study or a one semester course in Fourier analysis, included are detailed examples and exercises.
- Explains how ideas from harmonic analysis are used in the analysis of various important singular integral transforms.
- Clean and systematic presentation of theorems and proofs.
- Ideal for self-study or a course in Fourier analysis.Fundamental concepts
Fourier series
Schwartz spaces S(ℝn)
Distribution functions
Three-fold approach to the Hilbert transform
Hilbert transform in L2(ℝ)
Embedding and strong Lp boundedness for the Hilbert transform
Riesz transform