Hardy Spaces on Homogeneous Groups by Gerald B. Folland, Elias M. Stein
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About this book :-
Hardy Spaces on Homogeneous Groups written by
Gerald B. Folland, Elias M. Stein
The object of this monograph Is to give an exposition of the real-variable theory of Hardy spaces (H^p spaces). This theory has attracted considerable attention in recent years because it led to a better understanding in IR^n of such related topics as singular integrals, multiplier operators, maximal functions, and real-variable methods generally. Because of its fruitful development it seems to us that a systematic exposition of some of the main parts of this theory is now desirable. There are, however, good reasons why in addition the theory should be recast in the more general setting where the underlying IR^n is replaced by a homogeneous group. The justification for this wider scope, both in terms of the structure of the theory and its applications, will be described in more detail below.
(Gerald B. Folland, Elias M. Stein)
Book Detail :-
Title: Hardy Spaces on Homogeneous Groups
Edition:
Author(s): Gerald B. Folland, Elias M. Stein
Publisher: Princeton University Press; University of Tokyo Press
Series: Mathematical notes 28
Year: 1982
Pages: 299
Type: PDF
Language: English
ISBN: 069108310X,9780691083100
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 :-
Hardy Spaces on Homogeneous Groups written by
Gerald B. Folland, Elias M. Stein
cover the following topics.
0. Introduction
1. Background on Homogenous Groups
2. Maximal Functions and Atoms Notes and Refrences
3. Decomposition and Interpolation Theorems
4. Other Maximal Function Characterizations of HP
5. Duals of HP Spaces: Campanato Spaces
6. Convolution Operators of HP
7. Charatrization of HP by Square Functions: The Lusin and Littlewood-Paley Functions
8. Boundary Value Problems
Bibliography
Index of Terminology
Index of Notation
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