Loukas Grafakos

Fundamentals of Fourier Analysis

• Broschiertes Buch

Produktbeschreibung

1 Introductory Material.- 2 Fourier Transforms, Tempered Distributions, Approximate Identities.- 3 Singular Integrals.- 4 Vector-Valued Singular Integrals and Littlewood-Paley Theory.- 5 Fractional Integrability or Differentiability and Multiplier Theorems.- 6 Bounded Mean Oscillation.- 7 Hardy Spaces.- 8 Weighted Inequalities.- Historical Notes.- Appendix A Orthogonal Matrices.- Appendix B Subharmonic Functions.- Appendix C Poisson Kernel on the Unit Strip.- Appendix D Density for Subadditive Operators.- Appendix E Transposes and Adjoints of Linear Operators.- Appendix F Faa di Bruno Formula.- Appendix G Besicovitch Covering Lemma.- Glossary.- References.- Index.

Produktdetails

• Verlag: Springer / Springer International Publishing AG / Springer Nature Switzerland
• Seitenzahl: 424
• Erscheinungstermin: 23. Juli 2025
• Englisch
• Abmessung: 235mm x 155mm x 23mm
• Gewicht: 639g
• ISBN-13: 9783031565021
• ISBN-10: 3031565029
• Artikelnr.: 75828228

Autorenporträt

Loukas Grafakos is the Mahala and Rose Houchins Distinguished Professor of Mathematics at the University of Missouri at Columbia. He is author of 3 Graduate Texts in Mathematics: Classical Fourier Analysis (GTM 249), Modern Fourier Analysis (GTM 250), and Fundamentals of Fourier Analysis (GTM 302). His research is in Harmonic Analysis.

Inhaltsangabe

1 Introductory Material.
2 Fourier Transforms, Tempered Distributions, Approximate Identities.
3 Singular Integrals.
4 Vector
Valued Singular Integrals and Littlewood
Paley Theory.
5 Fractional Integrability or Differentiability and Multiplier Theorems.
6 Bounded Mean Oscillation.
7 Hardy Spaces.
8 Weighted Inequalities.
Historical Notes.
Appendix A Orthogonal Matrices.
Appendix B Subharmonic Functions.
Appendix C Poisson Kernel on the Unit Strip.
Appendix D Density for Subadditive Operators.
Appendix E Transposes and Adjoints of Linear Operators.
Appendix F Faa di Bruno Formula.
Appendix G Besicovitch Covering Lemma.
Glossary.
References.
Index.

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1 Introductory Material.- 2 Fourier Transforms, Tempered Distributions, Approximate Identities.- 3 Singular Integrals.- 4 Vector-Valued Singular Integrals and Littlewood-Paley Theory.- 5 Fractional Integrability or Differentiability and Multiplier Theorems.- 6 Bounded Mean Oscillation.- 7 Hardy Spaces.- 8 Weighted Inequalities.- Historical Notes.- Appendix A Orthogonal Matrices.- Appendix B Subharmonic Functions.- Appendix C Poisson Kernel on the Unit Strip.- Appendix D Density for Subadditive Operators.- Appendix E Transposes and Adjoints of Linear Operators.- Appendix F Faa di Bruno Formula.- Appendix G Besicovitch Covering Lemma.- Glossary.- References.- Index.

Rezensionen

This book provides an introduction to Fourier analysis on Euclidean spaces intended for students who have completed first-year graduate courses in real and complex analysis. The text is self-contained and complete with numerous exercises in each section and seven appendices. (Cody B. Stockdale, Mathematical Reviews, May, 2025)

The well-written monograph is intended to serve the purposes of a two-semester course. ... this textbook is very useful for graduate students in mathematics and a convenient reference for researchers working on multi-dimensional Fourier analysis. (Manfred Tasche, zbMATH 1551.42001, 2025)