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Continuity. --- Scholasticism. --- Aristotle.

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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.

Functions of real variables. --- Harmonic analysis. --- Singular integrals. --- Multiplicateurs (analyse mathématique) --- Multipliers (Mathematical analysis) --- Functional analysis --- Harmonic analysis. Fourier analysis --- Functions of real variables --- Harmonic analysis --- Singular integrals --- Fonctions de variables réelles --- Analyse harmonique --- Intégrales singulières --- Fonctions de plusieurs variables réelles --- Calcul différentiel --- Functions of several real variables --- Differential calculus --- 517.518.5 --- Integrals, Singular --- Integral operators --- Integral transforms --- Analysis (Mathematics) --- Functions, Potential --- Potential functions --- Banach algebras --- Calculus --- Mathematical analysis --- Mathematics --- Bessel functions --- Fourier series --- Harmonic functions --- Time-series analysis --- Real variables --- Functions of complex variables --- 517.518.5 Theory of the Fourier integral --- Theory of the Fourier integral --- A priori estimate. --- Analytic function. --- Banach algebra. --- Banach space. --- Basis (linear algebra). --- Bessel function. --- Bessel potential. --- Big O notation. --- Borel measure. --- Boundary value problem. --- Bounded function. --- Bounded operator. --- Bounded set (topological vector space). --- Bounded variation. --- Boundedness. --- Cartesian product. --- Change of variables. --- Characteristic function (probability theory). --- Characterization (mathematics). --- Commutative property. --- Complex analysis. --- Complex number. --- Continuous function (set theory). --- Continuous function. --- Convolution. --- Derivative. --- Difference "ient. --- Difference set. --- Differentiable function. --- Dimension (vector space). --- Dimensional analysis. --- Dirac measure. --- Dirichlet problem. --- Distribution function. --- Division by zero. --- Dot product. --- Dual space. --- Equation. --- Existential quantification. --- Family of sets. --- Fatou's theorem. --- Finite difference. --- Fourier analysis. --- Fourier series. --- Fourier transform. --- Function space. --- Green's theorem. --- Harmonic function. --- Hilbert space. --- Hilbert transform. --- Homogeneous function. --- Infimum and supremum. --- Integral transform. --- Interpolation theorem. --- Interval (mathematics). --- Linear map. --- Lipschitz continuity. --- Lipschitz domain. --- Locally integrable function. --- Marcinkiewicz interpolation theorem. --- Mathematical induction. --- Maximal function. --- Maximum principle. --- Mean value theorem. --- Measure (mathematics). --- Modulus of continuity. --- Multiple integral. --- Open set. --- Order of integration. --- Orthogonality. --- Orthonormal basis. --- Partial derivative. --- Partial differential equation. --- Partition of unity. --- Periodic function. --- Plancherel theorem. --- Pointwise. --- Poisson kernel. --- Polynomial. --- Real variable. --- Rectangle. --- Riesz potential. --- Riesz transform. --- Scientific notation. --- Sign (mathematics). --- Singular integral. --- Sobolev space. --- Special case. --- Splitting lemma. --- Subsequence. --- Subset. --- Summation. --- Support (mathematics). --- Theorem. --- Theory. --- Total order. --- Unit vector. --- Variable (mathematics). --- Zero of a function. --- Fonctions de plusieurs variables réelles --- Calcul différentiel --- Multiplicateurs (analyse mathématique)