Discrete Analogues in Harmonic Analysis

Harmonic analytic preliminaries: Tools
On oscillation and convergence
The linear theory
Discrete analogues in harmonic analyis: Radon transforms, I: Bourgain's maximal functions on $/ell^2(/mathbb{Z})$
Random pointwise ergodic theory
An application to discrete Ramsey theory
Bourgain's $/ell(/mathbb{Z})$=argument, revisited
Discrete analogues in harmonic analysis: Radon transforms, II: Ionescu-Wainger theory
Establishing Ionescu-Wainger theory
The spherical maximal function
The lacunary spherical maximal function
Disctrete improving inequalities
Discrete analogues in harmonic analysis: Maximally modulated singular integrals: Monomial ``Carleson'' operators
Maximally modulated singular integrals: A theorem of Stein and Wainger
Discrete analogues in harmonic analysis: An introduction to multilinear theory: Bilinear considerations
Arithmetic Sobolev estimates, examples
Conclusion and appendices: Further directions
Remembering my collaboration with Stein and Bourgain-M. Mirek
Introduction to additive combinatorics
Oscillatory integrals and exponential sums
Bibliography
Index