Classical and multilinear harmonic analysis

著者

書誌事項

Classical and multilinear harmonic analysis

Camil Muscalu, Wilhelm Schlag

（Cambridge studies in advanced mathematics, 137-138）

Cambridge University Press, 2013

  • v. 1 : hardback
  • v. 2 : hardback

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注記

Includes bibliographical references and indexes

内容説明・目次

巻冊次

v. 1 : hardback ISBN 9780521882453

内容説明

This two-volume text in harmonic analysis introduces a wealth of analytical results and techniques. It is largely self-contained and will be useful to graduate students and researchers in both pure and applied analysis. Numerous exercises and problems make the text suitable for self-study and the classroom alike. This first volume starts with classical one-dimensional topics: Fourier series; harmonic functions; Hilbert transform. Then the higher-dimensional Calderon-Zygmund and Littlewood-Paley theories are developed. Probabilistic methods and their applications are discussed, as are applications of harmonic analysis to partial differential equations. The volume concludes with an introduction to the Weyl calculus. The second volume goes beyond the classical to the highly contemporary and focuses on multilinear aspects of harmonic analysis: the bilinear Hilbert transform; Coifman-Meyer theory; Carleson's resolution of the Lusin conjecture; Calderon's commutators and the Cauchy integral on Lipschitz curves. The material in this volume has not previously appeared together in book form.

目次

  • Preface
  • Acknowledgements
  • 1. Fourier series: convergence and summability
  • 2. Harmonic functions, Poisson kernel
  • 3. Conjugate harmonic functions, Hilbert transform
  • 4. The Fourier Transform on Rd and on LCA groups
  • 5. Introduction to probability theory
  • 6. Fourier series and randomness
  • 7. Calderon-Zygmund theory of singular integrals
  • 8. Littlewood-Paley theory
  • 9. Almost orthogonality
  • 10. The uncertainty principle
  • 11. Fourier restriction and applications
  • 12. Introduction to the Weyl calculus
  • References
  • Index.
巻冊次

v. 2 : hardback ISBN 9781107031821

内容説明

This two-volume text in harmonic analysis introduces a wealth of analytical results and techniques. It is largely self-contained and useful to graduates and researchers in pure and applied analysis. Numerous exercises and problems make the text suitable for self-study and the classroom alike. The first volume starts with classical one-dimensional topics: Fourier series; harmonic functions; Hilbert transform. Then the higher-dimensional Calderon-Zygmund and Littlewood-Paley theories are developed. Probabilistic methods and their applications are discussed, as are applications of harmonic analysis to partial differential equations. The volume concludes with an introduction to the Weyl calculus. The second volume goes beyond the classical to the highly contemporary and focuses on multilinear aspects of harmonic analysis: the bilinear Hilbert transform; Coifman-Meyer theory; Carleson's resolution of the Lusin conjecture; Calderon's commutators and the Cauchy integral on Lipschitz curves. The material in this volume has not previously appeared together in book form.

目次

  • Preface
  • Acknowledgements
  • 1. Leibniz rules and gKdV equations
  • 2. Classical paraproducts
  • 3. Paraproducts on polydiscs
  • 4. Calderon commutators and the Cauchy integral
  • 5. Iterated Fourier series and physical reality
  • 6. The bilinear Hilbert transform
  • 7. Almost everywhere convergence of Fourier series
  • 8. Flag paraproducts
  • 9. Appendix: multilinear interpolation
  • Bibliography
  • Index.

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