Title An Introduction to Singular Integrals
Author Jacques Peyrière
ISBN 9781611975413
List price USD 59.00
Price outside India Available on Request
Original price
Binding Paperback
No of pages 116
Book size 178 x 254 mm
Publishing year 2018
Original publisher SIAM - Society for Industrial and Applied Mathematics (Eurospan Group)
Published in India by .
Exclusive distributors Viva Books Private Limited
Sales territory India, Sri Lanka, Bangladesh, Pakistan, Nepal, .
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In just over 100 pages, this book provides basic, essential knowledge of some of the tools of real analysis: the Hardy–Littlewood maximal operator, the Calderón–Zygmund theory, the Littlewood–Paley theory, interpolation of spaces and operators, and the basics of H1 and BMO spaces. This concise text offers brief proofs and exercises of various difficulties designed to challenge and engage students.

An Introduction to Singular Integrals is meant to give first-year graduate students in Fourier analysis and partial differential equations an introduction to harmonic analysis. While some background material is included in the appendices, readers should have a basic knowledge of functional analysis, some acquaintance with measure and integration theory, and familiarity with the Fourier transform in Euclidean spaces.



Chapter 1: The Hardy–Littlewood maximal operator • The Hardy–Littlewood operator • The Lebesgue derivation theorem • Regular families • Control of some convolutions • Exercises

Chapter 2: Principal values, and some Fourier transforms • Operators commuting with translations • Principal values • Some Fourier transforms • Homogeneous kernels • Exercises

Chapter 3: The Calderón–Zygmund theory • The dyadic cubes • The Calderón–Zygmund decomposition • Singular integrals • Exercises

Chapter 4: The Littlewood–Paley theory • Vector-valued singular integrals • The Littlewood–Paley inequalities • The Marcinkiewicz multiplier theorem • Exercises

Chapter 5: Higher Riesz transforms • Spherical harmonics • Higher Riesz transforms • Nonsmooth kernels • Exercises

Chapter 6: BMO and H1 • The BMO space • The H1 (Rn) space • Duality of H1–BMO • Exercises

Chapter 7: Singular integrals on other groups • The torus • Z • Some totally disconnected groups • Exercises

Chapter 8: Interpolation • Real methods • Complex methods • Exercises

A. Background material • Vector-valued integrals • Convolution • Polar coordinates • Distribution functions and weak Lp spaces • Laplace transform • Khintchine inequalities • Exercises

B. Notation and conventions • Glossary of notation and symbols • Conventions




About the Author:

Jacques Peyrière is an emeritus professor of mathematics at Université Paris-Sud (Orsay). He has been head of the Equipe d’Analyse Harmonique (a CNRS team) there for 10 years. Professor Peyrière has published two books and more than 60 articles on harmonic analysis and related topics in mathematical journals, including Duke Mathematical Journal, Advances in Mathematics, and Probability Theory and Related Fields. His research interests are harmonic analysis, probability theory, and fractals.

Target Audience:

Useful for first-year graduate students in Fourier analysis and partial differential equations.

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