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The E. M. Stein Lectures on Hardy Spaces (Paperback, 1st ed. 2023)
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The E. M. Stein Lectures on Hardy Spaces (Paperback, 1st ed. 2023)
Series: Lecture Notes in Mathematics, 2326
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The book The E. M. Stein Lectures on Hardy Spaces is based on a
graduate course on real variable Hardy spaces which was given by
E.M. Stein at Princeton University in the academic year 1973-1974.
Stein, along with C. Fefferman and G. Weiss, pioneered this subject
area, removing the theory of Hardy spaces from its traditional
dependence on complex variables, and to reveal its real-variable
underpinnings. This book is based on Steven G. Krantz's notes from
the course given by Stein. The text builds on Fefferman's theorem
that BMO is the dual of the Hardy space. Using maximal functions,
singular integrals, and related ideas, Stein offers many new
characterizations of the Hardy spaces. The result is a rich
tapestry of ideas that develops the theory of singular integrals to
a new level. The final chapter describes the major developments
since 1974. This monograph is of broad interest to graduate
students and researchers in mathematical analysis. Prerequisites
for the book include a solid understanding of real variable theory
and complex variable theory. A basic knowledge of functional
analysis would also be useful.
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