Discrete Analogues in Harmonic Analysis: Bourgain, Stein, and Beyond

ISBN-13: 9781470471743 / Miękka / 2023 / 542 str.

Ben Krause

Spis treści

• Harmonic analytic preliminaries: Tools
• On oscillation and convergence
• The linear theory
• Discrete analogues in harmonic analyis: Radon transforms, I: Bourgain's maximal functions on $\ell^2(\mathbb)$
• Random pointwise ergodic theory
• An application to discrete Ramsey theory
• Bourgain's $\ell(\mathbb)$=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