Representation Theorems in Hardy Spaces

Preface; 1. Fourier series; 2. Abel–Poisson means; 3. Harmonic functions in the unit disc; 4. Logarithmic convexity; 5. Analytic functions in the unit disc; 6. Norm inequalities for the conjugate function; 7. Blaschke products and their applications; 8. Interpolating linear operators; 9. The Fourier transform; 10. Poisson integrals; 11. Harmonic functions in the upper half plane; 12. The Plancherel transform; 13. Analytic functions in the upper half plane; 14. The Hilbert transform on R; A. Topics from real analysis; B. A panoramic view of the representation theorems; Bibliography; Index.