Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals 1st Edition by Elias M. Stein | (PDF) Free Download

Description

This book contains an exposition of some of the main developments of the last twenty years in the following areas of harmonic analysis: singular integral and pseudo-differential operators, the theory of Hardy spaces, Lsup estimates involving oscillatory integrals and Fourier integral operators, relations of curvature to maximal inequalities, and connections with analysis on the Heisenberg group.

User’s Reviews

Editorial Reviews: Review “Elias M. Stein, Winner of the 2005 Stefan Bergman Prize, American Mathematical Society””Elias M. Stein, Winner of the 1998 Wolf Prize for Mathematics, the Wolf Foundation” From the Back Cover This book contains an exposition of some of the main developments of the last twenty years in the following areas of harmonic analysis: singular integral and pseudo-differential operators, the theory of Hardy spaces, L(superscript p) estimates involving oscillatory integrals and Fourier integral operators, relations of curvature to maximal inequalities, and connections with analysis on the Heisenberg group. About the Author Elias M. Stein is Professor of Mathematics at Princeton University. Read more

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This is an absolutely brilliant book on the subject ; very demanding but the richness is so great and up to date that it would be a scandal to criticize anything ; the book is intended to graduate students in maths wanting to learn analysis; the book is written in such a way that it makes it possible to learn entirely at home ! Giant !

⭐More than 700 pages of dense material with some very useful insides. The presentation of the material is very clear.

⭐Very useful book in very good conditions

⭐If you get involved in analysis sooner or later you will have to read Elias Stein. Why? Because the core of analysis is harmonic analysis, and this man has been one of the leading experts in the field over at least 35 years, so, whatever branch of analysis you choose, Dr. Stein will be there.This thick book (695 pages) includes most of the topics in harmonic analysis which have been researched extensively during the last 20 years. It should be taken as a complement to Stein’s “Singular Integrals and Differentiability Properties of Functions” (1970) and Stein & Weiss’ “Introduction to Fourier Analysis on Euclidean Spaces” (1971).Its contents are: Real variable theory (covering lemmas, maximal function, generalized Calderón-Zygmund decomposition, etc.), maximal functions (vector-valued max. functions, Carlesson measures, etc.), Hardy spaces (characterization, atomic decomposition, singular integrals, etc.), H^1 and BMO (sharp function, interpolation, etc.), weighted inequalities (the class A_p, etc.), Fourier transform, almost orthogonality, oscillatory integrals, maximal operators, maximal averages, the Heisenberg group.The style is concise and presents motivation for each topic. Includes excercises – called “further results” – which are short research topics on their own, and an extensive list of references. The cloth bound is lovely.Superb book; a must in every analyst’s library.Please check my other reviews (just click on my name above).

⭐This is beautiful elegant mathematics. I have read much of this beautiful book and Stein and Weiss’s companion book on Singular Integrals. If you want to know harmonic analysis, own these and spend many hours with them.

⭐Good

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