Provides a complete description of representation theorems with direct proofs for both classes of Hardy spaces.

Professor Javad Mashreghi is Bonyan Research Chair in Mathematical Analysis in the Department of Mathematics and Statistics at Laval University, Quebec. He won the prestigious G. de B. Robinson Award of the Canadian Mathematical Society in 2004 for two long research papers published in the Canadian Journal of Mathematics. His research interests are complex and harmonic analysis and their applications in applied sciences.

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.