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

Aus der Reihe Developments in Mathematics
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157,99 € UVP 181,89 €

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Beschreibung

Produktdetails

Einband

Gebundene Ausgabe

Erscheinungsdatum

05.11.2022

Abbildungen

XXVIII, 924 p. 44 illus., 20 illus. in color.

Verlag

Springer

Seitenzahl

924

Maße (L/B/H)

24,1/16/5,6 cm

Gewicht

1572 g

Auflage

22001 Auflage 1st edition 2022

Sprache

Englisch

ISBN

978-3-031-05949-0

Beschreibung

Rezension

“The theory is developed in a consistent manner, and the motivation behind the results and tools is made clear to the reader. All of the main results and also a vast majority of the auxiliary results come with full and carefully written proofs, making the book highly self-contained. Thus this work can be a useful and enjoyable reference. …” (Juha Lehrbäck, Mathematical Reviews, August, 2024)

Produktdetails

Einband

Gebundene Ausgabe

Erscheinungsdatum

05.11.2022

Abbildungen

XXVIII, 924 p. 44 illus., 20 illus. in color.

Verlag

Springer

Seitenzahl

924

Maße (L/B/H)

24,1/16/5,6 cm

Gewicht

1572 g

Auflage

22001 Auflage 1st edition 2022

Sprache

Englisch

ISBN

978-3-031-05949-0

Herstelleradresse

Springer-Verlag KG
Sachsenplatz 4-6
1201 Wien
AT

Email: ProductSafety@springernature.com

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  • Produktbild: Geometric Harmonic Analysis I
  • Produktbild: Geometric Harmonic Analysis I

  • 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.