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This book includes 13 papers concerning some of the recent progress in the theory of function spaces and its applications. The involved function spaces include Morrey and weak Morrey spaces, Hardy-type spaces, John–Nirenberg spaces, Sobolev spaces, and Besov and Triebel–Lizorkin spaces on different underlying spaces, and they are applied in the study of problems ranging from harmonic analysis to potential analysis and partial differential equations, such as the boundedness of paraproducts and Calderón operators, the characterization of pointwise multipliers, estimates of anisotropic logarithmic potential, as well as certain Dirichlet problems for the Schrödinger equation.

expansive matrix --- (mixed-norm) Hardy space --- molecule --- Calderón–Zygmund operator --- real interpolation --- besov space --- meyer wavelet --- Euclidean space --- cube --- congruent cube --- BMO --- JNp --- (localized) John–Nirenberg–Campanato space --- Riesz–Morrey space --- vanishing John–Nirenberg space --- duality --- commutator --- commutators --- Riesz potential --- homogeneous group --- space of homogeneous type --- paraproduct --- T(1) theorem --- hardy space --- bilinear estimate --- Hajłasz–Sobolev space --- Hajłasz–Besov space --- Hajłasz–Triebel–Lizorkin space --- generalized smoothness --- Lebesgue point --- capacity --- pointwise multipliers --- Morrey spaces --- block spaces --- convexification --- Calderón operator --- Hardy’s inequality --- variable Lebesgue space --- local Morrey space --- local block space --- extrapolation --- anisotropy --- Hardy space --- continuous ellipsoid cover --- maximal function --- anisotropic log-potential --- optimal polynomial inequality --- annulus body --- dual log-mixed volume --- Sobolev spaces --- compact manifolds --- tensor bundles --- differential operators --- Triebel–Lizorkin space --- Hardy inequality --- uniform domain --- fractional Laplacian --- Schrödinger equation --- Morrey space --- Dirichlet problem --- metric measure space

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This book includes 13 papers concerning some of the recent progress in the theory of function spaces and its applications. The involved function spaces include Morrey and weak Morrey spaces, Hardy-type spaces, John–Nirenberg spaces, Sobolev spaces, and Besov and Triebel–Lizorkin spaces on different underlying spaces, and they are applied in the study of problems ranging from harmonic analysis to potential analysis and partial differential equations, such as the boundedness of paraproducts and Calderón operators, the characterization of pointwise multipliers, estimates of anisotropic logarithmic potential, as well as certain Dirichlet problems for the Schrödinger equation.

Research & information: general --- Mathematics & science --- expansive matrix --- (mixed-norm) Hardy space --- molecule --- Calderón–Zygmund operator --- real interpolation --- besov space --- meyer wavelet --- Euclidean space --- cube --- congruent cube --- BMO --- JNp --- (localized) John–Nirenberg–Campanato space --- Riesz–Morrey space --- vanishing John–Nirenberg space --- duality --- commutator --- commutators --- Riesz potential --- homogeneous group --- space of homogeneous type --- paraproduct --- T(1) theorem --- hardy space --- bilinear estimate --- Hajłasz–Sobolev space --- Hajłasz–Besov space --- Hajłasz–Triebel–Lizorkin space --- generalized smoothness --- Lebesgue point --- capacity --- pointwise multipliers --- Morrey spaces --- block spaces --- convexification --- Calderón operator --- Hardy’s inequality --- variable Lebesgue space --- local Morrey space --- local block space --- extrapolation --- anisotropy --- Hardy space --- continuous ellipsoid cover --- maximal function --- anisotropic log-potential --- optimal polynomial inequality --- annulus body --- dual log-mixed volume --- Sobolev spaces --- compact manifolds --- tensor bundles --- differential operators --- Triebel–Lizorkin space --- Hardy inequality --- uniform domain --- fractional Laplacian --- Schrödinger equation --- Morrey space --- Dirichlet problem --- metric measure space --- expansive matrix --- (mixed-norm) Hardy space --- molecule --- Calderón–Zygmund operator --- real interpolation --- besov space --- meyer wavelet --- Euclidean space --- cube --- congruent cube --- BMO --- JNp --- (localized) John–Nirenberg–Campanato space --- Riesz–Morrey space --- vanishing John–Nirenberg space --- duality --- commutator --- commutators --- Riesz potential --- homogeneous group --- space of homogeneous type --- paraproduct --- T(1) theorem --- hardy space --- bilinear estimate --- Hajłasz–Sobolev space --- Hajłasz–Besov space --- Hajłasz–Triebel–Lizorkin space --- generalized smoothness --- Lebesgue point --- capacity --- pointwise multipliers --- Morrey spaces --- block spaces --- convexification --- Calderón operator --- Hardy’s inequality --- variable Lebesgue space --- local Morrey space --- local block space --- extrapolation --- anisotropy --- Hardy space --- continuous ellipsoid cover --- maximal function --- anisotropic log-potential --- optimal polynomial inequality --- annulus body --- dual log-mixed volume --- Sobolev spaces --- compact manifolds --- tensor bundles --- differential operators --- Triebel–Lizorkin space --- Hardy inequality --- uniform domain --- fractional Laplacian --- Schrödinger equation --- Morrey space --- Dirichlet problem --- metric measure space

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The description for this book, Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems. (AM-105), Volume 105, will be forthcoming.

Calculus of variations --- Integrals, Multiple --- Differential equations, Elliptic --- Calcul des variations --- Equations différentielles elliptiques --- $ PDMC --- Multiple integrals --- Calculus of variations. --- Multiple integrals. --- Differential equations, Elliptic. --- Equations différentielles elliptiques --- Elliptic differential equations --- Elliptic partial differential equations --- Linear elliptic differential equations --- Differential equations, Linear --- Differential equations, Partial --- Double integrals --- Iterated integrals --- Triple integrals --- Integrals --- Probabilities --- Isoperimetrical problems --- Variations, Calculus of --- Maxima and minima --- A priori estimate. --- Analytic function. --- Boundary value problem. --- Coefficient. --- Compact space. --- Convex function. --- Convex set. --- Corollary. --- Counterexample. --- David Hilbert. --- Dense set. --- Derivative. --- Differentiable function. --- Differential geometry. --- Dirichlet integral. --- Dirichlet problem. --- Division by zero. --- Ellipse. --- Energy functional. --- Equation. --- Estimation. --- Euler equations (fluid dynamics). --- Existential quantification. --- First variation. --- Generic property. --- Harmonic function. --- Harmonic map. --- Hausdorff dimension. --- Hölder's inequality. --- I0. --- Infimum and supremum. --- Limit superior and limit inferior. --- Linear equation. --- Maxima and minima. --- Maximal function. --- Metric space. --- Minimal surface. --- Multiple integral. --- Nonlinear system. --- Obstacle problem. --- Open set. --- Partial derivative. --- Quantity. --- Semi-continuity. --- Singular solution. --- Smoothness. --- Sobolev space. --- Special case. --- Stationary point. --- Subsequence. --- Subset. --- Theorem. --- Topological property. --- Topology. --- Uniform convergence. --- Variational inequality. --- Weak formulation. --- Weak solution.

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This book has as its subject the boundary value theory of holomorphic functions in several complex variables, a topic that is just now coming to the forefront of mathematical analysis. For one variable, the topic is classical and rather well understood. In several variables, the necessary understanding of holomorphic functions via partial differential equations has a recent origin, and Professor Stein's book, which emphasizes the potential-theoretic aspects of the boundary value problem, should become the standard work in the field.Originally published in 1972.The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Mathematical potential theory --- Holomorphic functions --- Harmonic functions --- Holomorphic functions. --- Harmonic functions. --- Fonctions de plusieurs variables complexes. --- Functions of several complex variables --- Functions, Harmonic --- Laplace's equations --- Bessel functions --- Differential equations, Partial --- Fourier series --- Harmonic analysis --- Lamé's functions --- Spherical harmonics --- Toroidal harmonics --- Functions, Holomorphic --- Absolute continuity. --- Absolute value. --- Addition. --- Ambient space. --- Analytic function. --- Arbitrarily large. --- Bergman metric. --- Borel measure. --- Boundary (topology). --- Boundary value problem. --- Bounded set (topological vector space). --- Boundedness. --- Brownian motion. --- Calculation. --- Change of variables. --- Characteristic function (probability theory). --- Combination. --- Compact space. --- Complex analysis. --- Complex conjugate. --- Computation. --- Conformal map. --- Constant term. --- Continuous function. --- Coordinate system. --- Corollary. --- Cramer's rule. --- Determinant. --- Diameter. --- Dimension. --- Elliptic operator. --- Estimation. --- Existential quantification. --- Explicit formulae (L-function). --- Exterior (topology). --- Fatou's theorem. --- Function space. --- Green's function. --- Green's theorem. --- Haar measure. --- Half-space (geometry). --- Harmonic function. --- Hilbert space. --- Holomorphic function. --- Hyperbolic space. --- Hypersurface. --- Hölder's inequality. --- Invariant measure. --- Invertible matrix. --- Jacobian matrix and determinant. --- Line segment. --- Linear map. --- Lipschitz continuity. --- Local coordinates. --- Logarithm. --- Majorization. --- Matrix (mathematics). --- Maximal function. --- Measure (mathematics). --- Minimum distance. --- Natural number. --- Normal (geometry). --- Open set. --- Order of magnitude. --- Orthogonal complement. --- Orthonormal basis. --- Parameter. --- Poisson kernel. --- Positive-definite matrix. --- Potential theory. --- Projection (linear algebra). --- Quadratic form. --- Quantity. --- Real structure. --- Requirement. --- Scientific notation. --- Sesquilinear form. --- Several complex variables. --- Sign (mathematics). --- Smoothness. --- Subgroup. --- Subharmonic function. --- Subsequence. --- Subset. --- Summation. --- Tangent space. --- Theorem. --- Theory. --- Total variation. --- Transitive relation. --- Transitivity. --- Transpose. --- Two-form. --- Unit sphere. --- Unitary matrix. --- Vector field. --- Vector space. --- Volume element. --- Weak topology.

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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)