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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
Geometric Harmonic Analysis I: A Sharp Divergence Theorem with Nontangential Pointwise Traces

Geometric Harmonic Analysis I: A Sharp Divergence Theorem with Nontangential Pointwise Traces

Mitrea, Dorina
Mitrea, Irina
Mitrea, Marius

Hardcover

Series: Developments in Mathematics, Book 72

General Mathematics

ISBN10: 3031059492
ISBN13: 9783031059490
Publisher: Springer Nature
Published: Nov 5 2022
Pages: 924
Weight: 3.30
Height: 1.94 Width: 6.14 Depth: 9.21
Language: English
Prefacing this Series.- Statement of Main Results Concerning the Divergence Theorem.- Examples, Counterexamples, and Additional Perspectives.- Measure Theoretical and Topological Rudiments.- Sets of Locally Finite Perimeter and Other Categories of Euclidean Sets.- Tools from Harmonic Analysis.- Quasi-Metric Spaces and Spaces of Homogenous Type.- Open Sets with Locally Finite Surface Measures and Boundary Behavior.- Proofs of Main Results Pertaining to the Divergence Theorem.- II: Function Spaces Measuring Size and Smoothness on Rough Sets.- Preliminary Functional Analytic Matters.- Selected Topics in Distribution Theory.- Hardy Spaces on Ahlfors Regular Sets.- Morrey-Campanato Spaces, Morrey Spaces, and Their Pre-Duals on Ahlfors Regular Sets.- Besov and Triebel-Lizorkin Spaces on Ahlfors Regular Sets.- Boundary Traces from Weighted Sobolev Spaces in Besov Spaces.- Besov and Triebel-Lizorkin Spaces in Open Sets.- Strong and Weak Normal Boundary Traces of Vector Fields in Hardy and Morney Spaces.- Sobolev Spaces on the Geometric Measure Theoretic boundary of Sets of Locally Finite Perimeter.- III: Integral Representations Calderón-Zygmund Theory, Fatou Theorems, and Applications to Scattering.- Integral Representations and Integral Identities.- Calderón-Zygmund Theory on Uniformly Rectifiable Sets.- Quantitative Fatou-Type Theorems in Arbitrary UR Domains.- Scattering by Rough Obstacles.- IV: Boundary Layer Potentials on Uniformly Rectifiable Domains, and Applications to Complex Analysis.- Layer Potential Operators on Lebesgue and Sobolev Spaces.- Layer Potential Operators on Hardy, BMO, VMO, and Hölder Spaces.- Layer Potential Operators on Calderón, Morrey-Campanato, and Morrey Spaces.- Layer Potential Operators Acting from Boundary Besov and Triebel-Lizorkin Spaces.- Generalized double Layers in Uniformly Rectifiable Domains.- Green Formulas and Layer Potential Operators for the Stokes System.- Applications to Analysis in Several Complex Variables.- V: Fredholm Theory and Finer Estimates for Integral Operators, with Applications to Boundary Problems.- Abstract Fredholm Theory.- Distinguished Coefficient Tensors.- Failure of Fredholm Solvability for Weakly Elliptic Systems.- Quantifying Global and Infinitesimal Flatness.- Norm Estimates and Invertibility Results for SIO's on Unbounded Boundaries.- Estimating Chord-Dot-Normal SIO's on Domains with Compact Boundaries.- The Radon-Carleman Problem.- Fredholmness and Invertibility of Layer Potentials on Compact Boundaries.- Green Functions and Uniqueness for Boundary Problems for Second-Order Systems.- Green Functions and Poisson Kernels for the Laplacian.- Boundary Value Problems for Elliptic Systems in Rough Domains.

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