Modern Fourier Analysis

ISBN-13: 9781493950782 / Angielski / Miękka / 2016 / 624 str.

Loukas Grafakos

Opis

The primary goal of this book is to present the theoretical foundation of the field of Euclidean Harmonic analysis. This book is Modern in that is contains more recent topics such as function spaces, atomic decompositions, singular integrals of nonconvolution type, and weighted inequalities. This book is mainly addressed to graduate students in mathematics. The prerequisites are satisfactory completion of courses in real and complex variables, and knowledge of classical Fourier analysis topics. This book is intended to present the selected topics in depth and stimulate further study. This third edition includes a new chapter entitled "Multilinear Harmonic Analysis," which includes sections on multilinear operators, multilinear interpolation, multilinear multiplier operators, Calderon-Zygmund operators of several functions, and multiple weights and weighted norm inequalities. The new chapter will tie nicely with the material in chapters 8, 9, and 10, and the author may add a new section in this chapter applying the techniques of chapter 11 in the context of multilinear harmonic analysis. In addition to a new chapter, the third edition contains 1000 different corrections and improvements in the existing text, more examples and applications, new and more relevant hints for the existing exercises, about 20-30 new exercises in the existing chapters, and improved references.

Recenzje

"The most up-to-date account of the most important developments in the area. ... It has to be pointed out that the hard ones usually come with a good hint, which makes the book suitable for self-study, especially for more motivated students. That being said, the book provides a good reference point for seasoned researchers as well." (Atanas G. Stefanov, Mathematical Reviews, August, 2015)

Spis treści

Preface.- Smoothness and Function Spaces.- BMO and Carleson Measures.- Singular Integrals of Nonconvolution Type.- Weighted Inequalities.- Boundedness and Convergence of Fourier Integrals.- Time-Frequency Analysis and the Carleson-Hunt Theorem.- Multilinear Harmonic Analysis.- Glossary.- References.- Index.

O autorze

Loukas Grafakos is a Professor of Mathematics at the University of Missouri at Columbia.

Blurb

This text is addressed to graduate students in mathematics and to interested researchers who wish to acquire an in depth understanding of Euclidean Harmonic analysis. The text covers modern topics and techniques in function spaces, atomic decompositions, singular integrals of nonconvolution type, and the boundedness and convergence of Fourier series and integrals. The exposition and style are designed to stimulate further study and promote research. Historical information and references are included at the end of each chapter.

This third edition includes a new chapter entitled "Multilinear Harmonic Analysis" which focuses on topics related to multilinear operators and their applications. Sections 1.1 and 1.2 are also new in this edition. Numerous corrections have been made to the text from the previous editions and several improvements have been incorporated, such as the adoption of clear and elegant statements. A few more exercises have been added with relevant hints when necessary.

Reviews from the Second Edition:

“The books cover a large amount of mathematics. They are certainly a valuable and useful addition to the existing literature and can serve as textbooks or as reference books. Students will especially appreciate the extensive collection of exercises.”

—Andreas Seeger, Mathematical Reviews

“The exercises at the end of each section supplement the material of the section nicely and provide a good chance to develop

additional intuition and deeper comprehension. The historical notes in each chapter are intended to provide an account of past research as well as to suggest directions for further investigation. The volume is mainly addressed to graduate students who wish to study harmonic analysis.”

—Leonid Golinskii, zbMATH