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**About this book :- **
**Topics in Harmonic Analysis, Related to the Littlewood-Paley Theory ** written by
** Elias M. Stein **

Elias M. Stein purpose in these lectures was two-fold: First, to give a new approach to that part of harmonic analysis which for .tl:re-sake of simplicity we refer to as the "Littlewood-Paley Theory." The techniques that are used lead to a wide generalization of results hitherto restricted to an and other special contexts.

Elias M. Stein's second aim was to give the interested student a rapid (although admittedly sketchy) introduction to various areas in analysis, in particular some elements of Lie groups, almost everywhere limit theorems in the context of martingales, and complex interpolation of operators.

(Elias M. Stein)

**Book Detail :- **
** Title: ** Topics in Harmonic Analysis, Related to the Littlewood-Paley Theory
** Edition: **
** Author(s): ** Elias M. Stein
** Publisher: ** Princeton University Press
** Series: **
** Year: ** 1970
** Pages: ** 153
** Type: ** PDF
** Language: ** English
** ISBN: ** 0691080674,9780691080673
** Country: ** US

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**About Author :- **

Author ** Elias Menachem Stein ** was an American mathematician who was famous because of his work in the field of harmonic analysis. He was professor of Mathematics at Princeton University from 1963 until his death in 2018.

Author ** Menachem Stein ** was born in Antwerp Belgium, to Elkan Stein and Chana Goldman, Ashkenazi Jews from Belgium. In 1940, the Stein family move to the United States. He graduated from Stuyvesant High School in 1949, where he was classmates with future Fields Medalist Paul Cohen, before moving on to the University of Chicago for college. In 1955, Stein earned a Ph.D. from the University of Chicago under the direction of Antoni Zygmund. He began teaching in MIT in 1955, moved to the University of Chicago in 1958 as an assistant professor, and in 1963 became a full professor at Princeton.

Stein worked primarily in the field of harmonic analysis, and made contributions in both extending and clarifying Calderón–Zygmund theory. These include Stein interpolation, the Stein maximal principle, Stein complementary series representations, Nikishin–Pisier–Stein factorization in operator theory, the Tomas–Stein restriction theorem in Fourier analysis, the Kunze–Stein phenomenon in convolution on semisimple groups, the Cotlar–Stein lemma concerning the sum of almost orthogonal operators, and the Fefferman–Stein theory of the Hardy space and the space of functions of bounded mean oscillation.

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**Book Contents :- **
**Topics in Harmonic Analysis, Related to the Littlewood-Paley Theory ** written by
** Elias M. Stein **
cover the following topics.

Preface

Introduction

1. Lie Groups (A Review)

2. Littlewood-Paley Theory for a Compact Lie Group

3. General Symmetric Diffusion Semi-groups

4. The General Littlewood-Paley Theory

5. Further Illustrations

Bibliegraphical remarks

References

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