Morrey and Campanato meet Besov Lizorkin and Triebel 1st Edition by Wen Yuan, Winfried Sickel, Dachun Yang ISBN 3642146058 9783642146053 by Wen Yuan, Winfried Sickel, Dachun Yang (auth.) 9783642146053, 3642146058 instant download after payment.
Morrey and Campanato meet Besov Lizorkin and Triebel 1st Edition by Wen Yuan, Winfried Sickel, Dachun Yang - Ebook PDF Instant Download/Delivery: 3642146058, 9783642146053
Full download Morrey and Campanato meet Besov Lizorkin and Triebel 1st Edition after payment
Product details:
ISBN 10: 3642146058
ISBN 13: 9783642146053
Author: Wen Yuan, Winfried Sickel, Dachun Yang
Morrey and Campanato meet Besov Lizorkin and Triebel 1st Table of contents:
Chapter 1: Introduction: A Dialogue Between Function Spaces
- 1.1 The Landscape of Function Spaces in Analysis
- 1.2 Historical Context of Morrey and Campanato Spaces
- 1.3 The Rise of Besov and Lizorkin-Triebel Spaces
- 1.4 Why Do They Need to "Meet"? Motivations for Unifying Perspectives
- 1.5 Overview of Key Problems and Applications Addressed in the Book
- 1.6 Structure and Roadmap of the Book
Part I: Classical Pillars: Morrey and Campanato Spaces
Chapter 2: Foundations of Morrey Spaces
- 2.1 Definition and Basic Properties of Lp,λ(Ω)
- 2.2 Local and Global Morrey Spaces
- 2.3 Morrey Spaces and Hölder Continuity: Morrey's Embedding Theorem
- 2.4 Duality and Interpolation Properties
- 2.5 Regularity Theory for Elliptic PDEs in Morrey Spaces
Chapter 3: Campanato Spaces and Their Characterizations
- 3.1 Definition and Oscillation Properties of Lp,λ(Ω)
- 3.2 Campanato's Oscillation Lemma and its Significance
- 3.3 The Equivalence of Campanato Spaces and Hölder Spaces
- 3.4 Campanato Spaces and Bounded Mean Oscillation (BMO)
- 3.5 Regularity of Solutions to Variational Problems
Part II: Modern Tools: Besov and Lizorkin-Triebel Spaces
Chapter 4: Besov Spaces: A Multiscale Perspective
- 4.1 Littlewood-Paley Theory and Dyadic Decompositions
- 4.2 Definition of Besov Spaces Bp,qs(Rn) via Fourier Transform
- 4.3 Atomic and Molecular Decompositions
- 4.4 Embedding Theorems and Duality
- 4.5 Traces and Extensions of Besov Functions
Chapter 5: Lizorkin-Triebel Spaces: Generalizations and Unification
- 5.1 Definition of Lizorkin-Triebel Spaces Fp,qs(Rn)
- 5.2 Relation to Classical Spaces: Sobolev, Hölder, and Lp as Special Cases
- 5.3 Characterizations via Wavelets, Differences, and Pointwise Multipliers
- 5.4 Embedding and Interpolation Theory for Lizorkin-Triebel Spaces
- 5.5 Lizorkin-Triebel Spaces on Domains and Manifolds
Part III: The Meeting Point: Interconnections and Applications
Chapter 6: Embedding Theorems Between Classical and Modern Spaces
- 6.1 Morrey-Besov Embeddings: Bridging Local Regularity with Global Smoothness
- 6.2 Campanato-Lizorkin-Triebel Embeddings: Connecting Oscillation to Function Space Hierarchy
- 6.3 Optimal Embeddings and Counterexamples
- 6.4 The Role of Domain Properties (Regularity, Boundedness)
Chapter 7: New Characterizations and Equivalent Norms
- 7.1 Characterizations of Morrey Spaces via Wavelet Coefficients
- 7.2 Characterizations of Campanato Spaces using Dyadic Cubes and Oscillations
- 7.3 Pointwise and Local Characterizations of Besov and Lizorkin-Triebel Spaces
- 7.4 Unified Characterizations: Finding Common Ground in Diverse Definitions
Chapter 8: Regularity Theory for Partial Differential Equations
- 8.1 Elliptic PDEs: Higher Regularity in Besov and Lizorkin-Triebel Spaces
- 8.2 Parabolic PDEs: Time-Space Regularity and Evolution Equations
- 8.3 Nonlinear PDEs: Solutions in Critical Spaces
- 8.4 Applications to Fluid Dynamics (Navier-Stokes Equations) and Harmonic Analysis
- 8.5 Variational Problems and Function Spaces on Domains
Chapter 9: Fractional Calculus and Operators
- 9.1 Fractional Derivatives and Integrals in Besov and Lizorkin-Triebel Spaces
- 9.2 Singular Integral Operators and Calderón-Zygmund Theory
- 9.3 Riesz Potentials and Maximal Operators
- 9.4 Connections to Morrey Spaces and Fractional Integrability
Chapter 10: Further Directions and Open Problems
- 10.1 Weighted Spaces and Variable Exponents
- 10.2 Anisotropic Spaces
- 10.3 Quasiconformal Mappings and Function Spaces
- 10.4 Function Spaces in Abstract Settings (e.g., Metric Measure Spaces)
- 10.5 Future Research Directions
People also search for Morrey and Campanato meet Besov Lizorkin and Triebel 1st:
morrey and campanato meet besov
morrey and campanato meet besov lizorkin and triebel
dove cameron and cameron boyce best moments
d'morton and gifted rescue me
dove and cameron moments
Tags: Wen Yuan, Winfried Sickel, Dachun Yang, Morrey, Campanato
