Modern Fourier Analysis

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Springer Science & Business Media, Apr 28, 2009 - Mathematics - 507 pages
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The great response to the publication of the book Classical and Modern Fourier Analysishasbeenverygratifying.IamdelightedthatSpringerhasofferedtopublish the second edition of this book in two volumes: Classical Fourier Analysis, 2nd Edition, and Modern Fourier Analysis, 2nd Edition. These volumes are mainly addressed to graduate students who wish to study Fourier analysis. This second volume is intended to serve as a text for a seco- semester course in the subject. It is designed to be a continuation of the rst v- ume. Chapters 1–5 in the rst volume contain Lebesgue spaces, Lorentz spaces and interpolation, maximal functions, Fourier transforms and distributions, an introd- tion to Fourier analysis on the n-torus, singular integrals of convolution type, and Littlewood–Paley theory. Armed with the knowledgeof this material, in this volume,the reader encounters more advanced topics in Fourier analysis whose development has led to important theorems. These theorems are proved in great detail and their proofs are organized to present the ow of ideas. The exercises at the end of each section enrich the material of the corresponding section and provide an opportunity to develop ad- tional intuition and deeper comprehension. The historical notes in each chapter are intended to provide an account of past research but also to suggest directions for further investigation. The auxiliary results referred to the appendix can be located in the rst volume.
 

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Contents

I
1
II
2
III
6
IV
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V
12
VI
13
VII
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VIII
20
LXXXVII
238
LXXXVIII
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LXXXIX
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XC
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XCI
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XCII
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XCIII
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XCV
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IX
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CLXV
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CLXVI
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CLXVII
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CLXVIII
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CLXIX
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CLXX
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About the author (2009)

Loukas Grafakos" is a native of Athens, Greece. He earned his doctoral degree at UCLA and is currently a Professor of Mathematics at the University of Missouri. He has taught at Yale University and Washington University in St. Louis and he has also held visiting positions at the Mathematical Sciences Research Institute in Berkeley and the University of Pittsburgh. He has been named a Kemper Fellow for Excellence in Teaching and he has authored or co-authored over forty research articles in Fourier analysis. An avid traveler, he has visited over one hundred countries and has given many international lectures.

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