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Multi-parameter Singular Integrals. (AM-189), Volume I

Brian Street

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Princeton University Press img Link Publisher

Naturwissenschaften, Medizin, Informatik, Technik / Mathematik

Beschreibung

This book develops a new theory of multi-parameter singular integrals associated with Carnot-Carathéodory balls. Brian Street first details the classical theory of Calderón-Zygmund singular integrals and applications to linear partial differential equations. He then outlines the theory of multi-parameter Carnot-Carathéodory geometry, where the main tool is a quantitative version of the classical theorem of Frobenius. Street then gives several examples of multi-parameter singular integrals arising naturally in various problems. The final chapter of the book develops a general theory of singular integrals that generalizes and unifies these examples. This is one of the first general theories of multi-parameter singular integrals that goes beyond the product theory of singular integrals and their analogs. Multi-parameter Singular Integrals will interest graduate students and researchers working in singular integrals and related fields.

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Schlagwörter

Mathematical proof, Subset, Translational symmetry, Inverse function theorem, Topology, Change of variables, Equivalence class, Maximal function, Schwartz space, Square (algebra), Continuous function, Infimum and supremum, Existential quantification, Bilinear map, Partition of unity, Pseudo-differential operator, Vector space, Compact space, Parametrix, Boundedness, Corollary, Estimation, Parameter, Linear map, Frobenius theorem (differential topology), Lebesgue measure, Support (mathematics), Hilbert transform, Singular integral, Bounded operator, Sobolev space, Coefficient, Polynomial, Theorem, Linear combination, Bijection, Fundamental solution, Summation, Scientific notation, Schwartz kernel theorem, Trichotomy (mathematics), Tangent space, Characterization (mathematics), Special case, Subspace topology, Open set, Tensor product, Locally convex topological vector space, Bump function, Vector field, Borel measure, Frobenius theorem (real division algebras), Addition, Diffeomorphism, Convergence of random variables, Topological vector space, Universal property, Fourier inversion theorem, Geometry, Variable (mathematics), Lie algebra, Coarse topology, Division by zero, Heisenberg group, Fourier transform, Bounded set, Convolution, Bounded set (topological vector space), Theory, Lie group