E-Book Overview
The primary goal of these two volumes is to present the theoretical foundation of the field of Euclidean Harmonic analysis. The original edition was published as a single volume, but due to its size, scope, and the addition of new material, the second edition consists of two volumes. The present edition contains a new chapter on time-frequency analysis and the Carleson-Hunt theorem. The first volume contains the classical topics such as Interpolation, Fourier Series, the Fourier Transform, Maximal Functions, Singular Integrals, and Littlewood-Paley Theory. The second volume contains more recent topics such as Function Spaces, Atomic Decompositions, Singular Integrals of Nonconvolution Type, and Weighted Inequalities.
These volumes are mainly addressed to graduate students in mathematics and are designed for a two-course sequence on the subject with additional material included for reference. The prerequisites for the first volume are satisfactory completion of courses in real and complex variables. The second volume assumes material from the first. This book is intended to present the selected topics in depth and stimulate further study. Although the emphasis falls on real variable methods in Euclidean spaces, a chapter is devoted to the fundamentals of analysis on the torus. This material is included for historical reasons, as the genesis of Fourier analysis can be found in trigonometric expansions of periodic functions in several variables.
About the first edition:
"Grafakos's book is very user-friendly with numerous examples illustrating the definitions and ideas... The treatment is thoroughly modern with free use of operators and functional analysis. Morever, unlike many authors, Grafakos has clearly spent a great deal of time preparing the exercises."
- Kenneth Ross, MAA Online
E-Book Content
Graduate Texts in Mathematics 249 Editorial Board S. Axler K.A. Ribet Graduate Texts in Mathematics 1 TAKEUTI /Z ARING. Introduction to Axiomatic Set Theory. 2nd ed. 2 O XTOBY. Measure and Category. 2nd ed. 3 S CHAEFER . Topological Vector Spaces. 2nd ed. 4 H ILTON/S TAMMBACH. A Course in Homological Algebra. 2nd ed. 5 M AC L ANE. Categories for the Working Mathematician. 2nd ed. 6 H UGHES /P IPER. Projective Planes. 7 J.-P. S ERRE. A Course in Arithmetic. 8 TAKEUTI /Z ARING. Axiomatic Set Theory. 9 H UMPHREYS . Introduction to Lie Algebras and Representation Theory. 10 C OHEN. A Course in Simple Homotopy Theory. 11 C ONWAY. Functions of One Complex Variable I. 2nd ed. 12 B EALS . Advanced Mathematical Analysis. 13 A NDERSON/F ULLER. Rings and Categories of Modules. 2nd ed. 14 G OLUBITSKY/G UILLEMIN. Stable Mappings and Their Singularities. 15 B ERBERIAN. Lectures in Functional Analysis and Operator Theory. 16 W INTER. The Structure of Fields. 17 ROSENBLATT. Random Processes. 2nd ed. 18 H ALMOS . Measure Theory. 19 H ALMOS . A Hilbert Space Problem Book. 2nd ed. 20 H USEMOLLER. Fibre Bundles. 3rd ed. 21 H UMPHREYS . Linear Algebraic Groups. 22 BARNES /M ACK. An Algebraic Introduction to Mathematical Logic. 23 G REUB. Linear Algebra. 4th ed. 24 H OLMES . Geometric Functional Analysis and Its Applications. 25 H EWITT/S TROMBERG. Real and Abstract Analysis. 26 M ANES . Algebraic Theories. 27 K ELLEY. General Topology. 28 Z ARISKI /S AMUEL. CommutativeAlgebra. Vol. I. 29 Z ARISKI /S AMUEL. Commutative Algebra. Vol. II. 30 JACOBSON. Lectures in Abstract Algebra I. Basic Concepts. 31 JACOBSON. Lectures in Abstract Algebra II. Linear Algebra. 32 JACOBSON. Lectures in Abstract Algebra III. Theory of Fields and Galois Theory. 33 H IRSCH. Differential Topology. 34 S PITZER. Principles of Random Walk. 2nd ed. 35 A LEXANDER/W ERMER. Several Complex Variables and Banach Algebras. 3rd ed. 36 K ELLEY/N AMIOKA ET AL. Linear Topological Spaces. 37 M ONK. Mathematical Logic. 38 G RAUERT/F