New characterizations of Besov-Triebel-Lizorkin-Hausdorff spaces including coorbits and wavelets

DOI10.1007/s00041-012-9234-5zbMath1260.46026arXiv1103.5667OpenAlexW2038150216MaRDI QIDQ1759429

Yoshihiro Sawano, Wen Yuan, Da Chun Yang, Tino Ullrich, Yi Yu Liang

Publication date: 20 November 2012

Published in: The Journal of Fourier Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1103.5667

zbMATH Keywords

waveletsBesov-type spacesPeetre maximal functionslocal meansTriebel-Lizorkin-Hausdorff spacesTriebel-Lizorkin-type spacesBesov-Hausdorff spacesco-orbits

Mathematics Subject Classification ID

Nontrigonometric harmonic analysis involving wavelets and other special systems (42C40) Maximal functions, Littlewood-Paley theory (42B25) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35)

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Cites Work

• Unnamed Item
• Unnamed Item
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• Unnamed Item
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• Continuous characterizations of Besov-Lizorkin-Triebel spaces and new interpretations as coorbits
• Generalized coorbit space theory and inhomogeneous function spaces of Besov-Lizorkin-Triebel type
• The dyadic structure and atomic decomposition of \(Q\) spaces in several real variables
• Banach spaces related to integrable group representations and their atomic decompositions. I
• Characterizations of Besov-type and Triebel-Lizorkin-type spaces via maximal functions and local means
• Morrey potentials and harmonic maps
• Morrey spaces in harmonic analysis
• Banach spaces related to integrable group representations and their atomic decompositions. II
• A discrete transform and decompositions of distribution spaces
• A note on Besov-Morrey spaces and Triebel-Lizorkin-Morrey spaces
• A note on dyadic Hausdorff capacities
• A new class of function spaces connecting Triebel--Lizorkin spaces and \(Q\) spaces
• New Besov-type spaces and Triebel-Lizorkin-type spaces including \(Q\) spaces
• Decompositions of Besov-Hausdorff and Triebel-Lizorkin-Hausdorff spaces and their applications
• Morrey and Campanato meet Besov, Lizorkin and Triebel
• Wavelet characterization of Besov-Morrey and Triebel-Lizorkin-Morrey spaces
• New applications of Besov-type and Triebel-Lizorkin-type spaces
• Some new function spaces and their applications to harmonic analysis.
• Characterizations of Besov-Hardy-Sobolev spaces: A unified approach
• Describing functions: Atomic decompositions versus frames
• Weighted Hardy spaces
• Characterization of the Besov-Lipschitz and Triebel-Lizorkin spaces. The case \(q<1\)
• Some new tent spaces and duality theorems for fractional Carleson measures and \(Q_{\alpha}(\mathbb R^n)\).
• Decompositions of Besov-Morrey spaces and Triebel-Lizorkin-Morrey spaces
• Atomic and molecular decompositions of anisotropic Besov spaces
• Regularity of Morrey commutators
• Some properties of Morrey type Besov-Triebel spaces
• On functions of bounded mean oscillation
• Atomic decompositions of function spaces with Muckenhoupt weights, and some relation to fractal analysis
• On Restrictions and Extensions of the Besov and Triebel-Lizorkin Spaces with Respect to Lipschitz Domains
• Biorthogonal bases of compactly supported wavelets
• Anisotropic Hardy spaces and wavelets
• Decomposition systems for function spaces
• Wavelet bases and entropy numbers in weighted function spaces
• Q spaces of several real variables
• Relations among Besov-type spaces, Triebel–Lizorkin-type spaces and generalized Carleson measure spaces
• Coorbit space theory for quasi-Banach spaces
• Some Maximal Inequalities
• Nonlinear potential analysis on Morrey spaces and their capacities
• Atomic and molecular decompositions of anisotropic Triebel-Lizorkin spaces
• On the Solutions of Quasi-Linear Elliptic Partial Differential Equations
• Locally bounded linear topological spaces
• Holomorphic \(Q\) classes