This book contains papers presented at the Chicago Conference on Harmonic Analysis in 1981. The papers are compiled under topics, namely trigonometric series, singular integrals and pseudodifferential operators, hardy spaces, differentiation theory, and partial differential equations.
Table of Contents
Part One: Introductory Paper 1. The development of square functions in the work of A. Zygmund Part Two: Trigonometric Series 2. Convolution inequalities on the circle 3. A convolution structure and positivity of a generalized translation operator for the continuous q-Jacobi polynomials 4. Bernstein's inequality for finite intervals 5. Slow points of Gaussian processes 6. Notes on trigonometric polynomials 7. Certain function spaces connected with almost everywhere convergence of Fourier series 8. Exponential estimates in multiplier algebras Part Three: Fourier Analysis on R" And Real Analysis 9. On weighted fractional integrals 10. The density of the area integral 11. The Hardy-Littlewood maximal function on L(p, 1) 12. A note on the equivalence of AP and Sawyer's condition for equal weights 13. On the decomposition of L11(R) functions into humps 14. On inequalities of Carleson and Hunt 15. On the restriction of Fourier transforms to curves 16. Minimal smoothness for a bound on the Fourier transform of a surface measure Part Four: Singular Integrals and Pseudodifferential Operators 17. A generalized Herglotz-Bochner theorem and L2-weighted inequalities with finite measures 18. A geometric condition that implies the existence of certain singular integrals of Banach-spacevalued functions 19. Estimations L2 pour les noyaux singuliers 20. Vector valued inequalities for multipliers 21. On some Lp versions of the Helson-Szego theorem 22. Some topics in Calder6n-Zygmund theory 23. Singular integrals with kernels of mixed homogeneities 24. An application of singular integrals to a growth problem for entire functions of finite order Part Five: Hardy Spaces 25. On H in multiply connected domains 26. Two remarks about H1 and BMO on the bidisc 27. On the solution of the equation ∆mF = f FOR f ∈ Hp 28. Higher gradients and representations of lie groups 29. Interpolation between Hardy spaces 30. Weighted H1-BMO dualities 31. The Shilov and Bishop decompositions of H + C 32. A mod