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 modified Franklin system and higher-order spline systems on Rn as unconditional bases for Hardy spaces 33. A constructive proof of the Fefferman-Stein decomposition of BMO on simple martingales Part Six: Differentiation Theory 34. Relations between Peano derivatives and Marcinkiewicz integrals 35. Some results and open problems in differentiation of integrals 36. Tangential boundary behavior of harmonic extensions of Lp potentials 37. Strong differentials in Lp Part Seven: Partial Differential Equations 38. On the lack of L-estimates for solutions of elliptic systems or equations with complex coefficients 39. Boundary behavior of solutions to degenerate elliptic equations 40. Subelliptic eigenvalue problems 41. Summability and bounds for multipliers of elliptic operators 'on Rn 42. On the Dirichlet problem for higher-order equations 43. Lp-estimates for a singular hyperbolic equation 44. Mixed norm estimates for the Klein-Gordon equation Part Eight: Other Topics Related to Harmonic Analysis 45. Scattering and inverse scattering related to evolution equations 46. Norm inequalities for holomorphic functions of several complex variables 47. On the Radon transform and some of its generalizations 48. An addition theorem for Heisenberg harmonics 49. Sur les diffeomorphismes du cercle de nombre de rotation de type constant 50. Sur un probleme de Michael Herman 51. Minimal and maximal methods of interpolation of Banach spaces 52. A theorem of Khrushchev and Peller on restrictions of analytic functions having finite Dirichlet integral to closed subsets of the unit circumference 53. Sendembeddings in linear topological spaces 54. Diffusion on the loops 55. Weighted analogues of Nikolskii-type inequalities and their applications 56. An application of the approximation functional in interpolation theory 57. An analogue of the Fejer-Riesz theorem for the Dirichlet space 58. Potential theory and diffusion on Riemannian manifolds