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Classical and Multilinear Harmonic Analysis: Volume 2
About this book
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 CalderĂłnâZygmund and LittlewoodâPaley 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; CoifmanâMeyer theory; Carleson's resolution of the Lusin conjecture; CalderĂłn's commutators and the Cauchy integral on Lipschitz curves. The material in this volume has not previously appeared together in book form.
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Information
Table of contents
- Cover
- Series
- Title
- Copyright
- Contents
- Preface
- Acknowledgements
- 1 Leibnitz rules and the generalized Korteweg-de Vries equation
- 2 Classical paraproducts
- 3 Paraproducts on polydisks
- 4 CalderĂłn 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
- References
- Index