Contents Preface xiii Preliminaries xvii Chapter 1. Fourier Series and Integrals 1 §1. Fourier coefficients and series 1 §2. Criteria for pointwise convergence 2 §3. Fourier series of continuous functions 6 §4. Convergence in norm 8 §5. Summability methods 9 §6. The Fourier transform of L1 functions 11 §7. The Schwartz class and tempered distributions 12 §8. The Fourier transform on Lp, 1 p 2 15 §9. The convergence and summability of Fourier integrals 17 §10. Notes and further results 19 Chapter 2. The Hardy-Littlewood Maximal Function 25 §1. Approximations of the identity 25 §2. Weak-type inequalities and almost everywhere convergence 26 §3. The Marcinkiewicz interpolation theorem 28 §4. The Hardy-Littlewood maximal function 30
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