Bücher von Loukas Grafakos

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 "e;Multilinear Harmonic Analysis"e;, 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.

The primary goal of this book is to present the theoretical foundation of the field of Euclidean Harmonic analysis. This book contains the classical topics such as interpolation, Fourier series, the Fourier transform, maximal functions, singular integrals, and Littlewood-Paley theory. This book is mainly addressed to graduate students in mathematics. The prerequisites are satisfactory completion of courses in real and complex variables. This book is intended to present the selected topics in depth and stimulate further study. This third edition includes a new chapter entitled "e;Topics on Fourier series,"e; which includes sections on Gibbs phenomenon, summability methods and Jackson's theorem, Tauberian theorems, spherical Fourier inversion, and Fourier transforms on the line. The new chapter ties really well with the material in the existing chapter 3 "e;Fourier Analysis on the Torus"e; and will prepare the students for (the existing) chapter 4. 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.

Widely used graphics clarify both concrete and abstract concepts, helping students visualize the proofs of many results. Freely accessible solutions to every-other-odd exercise are posted to the book's Springer website.

This text is aimed at graduate students in mathematics and to interested researchers who wish to acquire an in depth understanding of Euclidean Harmonic analysis.

The coverage of topics and exposition style are designed to leave no gaps in understanding and stimulate further study.This third edition includes new Sections 3.5, 4.4, 4.5 as well as a new chapter on "Weighted Inequalities," which has been moved from GTM 250, 2nd Edition.