| Chapter 11 SPANS OF TRANSLATES. CLOSED IDEALS. CLOSED SUBALGEBRAS. BANACH ALGEBRAS 11.1 Closed Invariant Subspaces and Closed Ideals 11.2 The Structure of Closed Ideals and Related Topics 11.3 Closed Subalgebras 11.4 Banach Algebras and Their Applications Exercises Chapter 12 DISTRIBUTIONS AND MEASURES 12.1 Concerning CD 12.2 Definition and Examples of Distributions and Measures 12.3 Convergence of Distributions 12.4 Differentiation of Distributions 12.5 Fourier Coefficients and Fourier Series of Distributions 12.6 Convolutions of Distributions 12.7 More about M and Lp 12.8 Hilbert's Distribution and Conjugate Series 12.9 The Theorem of Marcel Riesz 12.10 Mean Convergence of Fourier Series in Lp （1 < p < ∞ ） 12.11 Pseudomeasures and Their Applications 12.12 Capacities and Beurling's Problem 12.13 The Dual Fomr of Bochner's Theorem Exercises Chapter 13 INTERPOLATION THEOREMS 13.1 Measure Spaces 13.2 0perators of Type （ p， q） 13.3 The Three Lines Theorem 13.4 The Riesz-Thorin Theorem 13.5 The Theorem of Hausdorff-Young 13.6 An Inequality of W. H. Young 13.7 0perators of Weak Type 13.8 The Marcinkiewicz Interpolation Theorem 13.9 Application to Conjugate Functions 13.10 Concerning a*f and s*f 13.11 Theorems of Hardv and Littlewood, Marcinkiewicz and Zygmund Exercises Chapter 14 CHANGING SIGNS OF FOURIER COEFFICIENTS 14.1 Harmonic Analysis on the Cantor Group 14.2 Rademacher Series Convergent in L2 14.3 Applications to Fourier Series 14.4 Comments on the Hausdorff-Young Theorem and Its Dual 14.5 A Look at Some Dual Results and Generalizations Exercises Chapter 15 LACUNARY FOURIER SERIES 15.1 Introduction of Sidon Sets 15.2 Construction and Examples of Sidon Sets 15.3 Further Inequalities Involving Sidon Sets 15.4 Counterexamples concerning the Parseval Formula and Hausdorff-Young Inequalities 15.5 Sets of Type （ p, q） and of Type A（ p） …… Chapter 16 MULTIPLIERS Biliography Research Publications Corrigenda to 2nd（Revised）Edition of Volume 1 Symbols Index |
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