Discrete analogues in harmonic analysis : Bourgain, Stein, and beyond

Author(s)

    • Krause, Ben

Bibliographic Information

Discrete analogues in harmonic analysis : Bourgain, Stein, and beyond

Ben Krause

(Graduate studies in mathematics, 224)

American Mathematical Society, c2022

  • : hardcover

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Note

Includes bibliographical references (p. 547-556) and index

Description and Table of Contents

Table of Contents

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

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