Singular Integrals, Herz-Type Function Spaces, and Boundary Problems
Springer International Publishing (Verlag)
978-3-032-12515-6 (ISBN)
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This monograph presents state-of-the-art results at the intersection of Harmonic Analysis, Functional Analysis, Geometric Measure Theory, and Partial Differential Equations, providing tools for treating elliptic boundary value problems for systems of PDE s in rough domains. Largely self-contained, it develops a comprehensive Calderón-Zygmund theory for singular integral operators on many Herz-type spaces, and their associated Hardy and Sobolev spaces, in the optimal geometric-measure theoretic setting of uniformly rectifiable sets. The present work highlights the effectiveness of boundary layer potential methods as a means of establishing well-posedness results for a wide family of boundary value problems, including Dirichlet, Neumann, Regularity, and Transmission Problems. Graduate students, researchers, and professional mathematicians interested in harmonic analysis and boundary problems will find this monograph a valuable resource in the field.
Introduction.- Preliminary Matters.- Beurling Algebras.- Beurling-Hardy Spaces.- Functions of Bounded Central Mean Oscillations.- Calderon-Zygmund Theory on Beurling-Hardy Spaces and BCMO_p Spaces.- Weakly Elliptic Systems and Layer Potentials on UR Domains.- Layer Potentials on Beurling-Hardy Spaces and BCMO_p Spaces.- Boundary Value Problems on Beurling-Hardy Spaces and BCMO_p Spaces.- Herz Spaces of First Generation.- Herz-type Hardy Spaces of First Generation.- Functions of (p,q)-Bounded Central Mean Oscillations.- Calderon-Zygmund Theory on First-Generation Herz-type Spaces.- Herz-Based Sobolev Spaces of First Generation.- Layer Potentials on Herz-type Spaces of First Generation and Invertibility Results.- Boundary Value Problems on Herz-type Spaces of First Generation.- Measure Theoretic Herz Spaces.- Calderon-Zygmund Theory on Herz Spaces of Second Generation.- Boundary Value Problems on Herz Spaces of Second Generation.- Inhomogeneous Herz-type Hardy Spaces of Second Generation.- Singular Integral Operators on Herz-type Hardy Spaces of Second Generation.- Layer Potentials and Boundary Problems on Herz-type Hardy Spaces of Second Generation.- A New Class of Herz-type Spaces, Singular Integrals, and Boundary Problems.- Herz Spaces on Bounded Ahlfors Regular Sets.- Boundary Value Problems in Domains with Compact Boundary.
| Erscheint lt. Verlag | 31.3.2026 |
|---|---|
| Reihe/Serie | Progress in Mathematics |
| Zusatzinfo | X, 291 p. 11 illus., 10 illus. in color. |
| Verlagsort | Cham |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| Schlagworte | boundary layer potentials • Boundary value problem • Calderón-Zygmund theory • Calderón–Zygmund theory • Composite Herz Space • Herz-type space • singular integral operators |
| ISBN-10 | 3-032-12515-4 / 3032125154 |
| ISBN-13 | 978-3-032-12515-6 / 9783032125156 |
| Zustand | Neuware |
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