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singular integrals, differentiability properties of functions [pdf]

Singular Integrals and Differentiability Properties of Functions by Elias M. Stein

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Singular Integrals and Differentiability Properties of Functions written by Elias M. Stein
Singular integrals are among the most interesting and important objects of study in analysis, one of the three main branches of mathematics. They deal with real and complex numbers and their functions. In this book, Princeton professor Elias Stein, a leading mathematical innovator as well as a gifted expositor, produced what has been called the most influential mathematics text in the last thirty-five years. One reason for its success as a text is its almost legendary presentation: Stein takes arcane material, previously understood only by specialists, and makes it accessible even to beginning graduate students. Readers have reflected that when you read this book, not only do you see that the greats of the past have done exciting work, but you also feel inspired that you can master the subject and contribute to it yourself.
Singular integrals were known to only a few specialists when Stein's book was first published. Over time, however, the book has inspired a whole generation of researchers to apply its methods to a broad range of problems in many disciplines, including engineering, biology, and finance.
Stein has received numerous awards for his research, including the Wolf Prize of Israel, the Steele Prize, and the National Medal of Science. He has published eight books with Princeton, including Real Analysis in 2005.
(Elias M. Stein)

Book Detail :-
Title: Singular Integrals and Differentiability Properties of Functions
Edition:
Author(s): Elias M. Stein
Publisher: Princeton University Press
Series: Princeton mathematical series
Year: 1970
Pages: 303
Type: PDF
Language: English
ISBN: 9780691080796,0691080798
Country: US
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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 :-
Singular Integrals and Differentiability Properties of Functions written by Elias M. Stein cover the following topics.
1. Some Fundamental Notions of Real Variable Theory
2. Singular Integrals
3. Riesz Tranforms, Poisson, Integrals and Spherical Harmonics
4. The Littlewood-Paley Theory and Multipliers
5. Differentiability Properties in Terms of Function Spaces
6. Extenssions and Restrictions
7. Returns to the Theory of Harmonic Functions
8. Differentiation of Functions
Appendix A: Some Inequilities
Appendix B: The Mareinkiewicz Interpolation Theorem
Appendix C: Some Elementry Properties of Harmonic Functions
Appendix D: Inequilities for Rademacher Functions
Bibliography
Index

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