Function spaces of Besov-type and Triebel-Lizorkin-type -- a survey

DOI10.1007/s11766-013-3205-8zbMath1299.46036OpenAlexW2073730957MaRDI QIDQ2016923

Wen Yuan, Da Chun Yang

Publication date: 30 June 2014

Published in: Applied Mathematics. Series B (English Edition) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11766-013-3205-8

zbMATH Keywords

dualBesov spaceembeddingatomwaveletlocal meanmoleculecomplex interpolationTriebel-Lizorkin spacePeetre maximal function

Mathematics Subject Classification ID

Maximal functions, Littlewood-Paley theory (42B25) Function spaces arising in harmonic analysis (42B35) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35)

Related Items (7)

Several equivalent characterizations of fractional Hajłasz-Morrey-Sobolev spaces ⋮ Generalized Morrey spaces and trace operator ⋮ Characterizations of product Hardy space associated to Schrödinger operators ⋮ On the stability to Keller-Segel system coupled with Navier-Stokes equations in Besov-Morrey spaces ⋮ Characterization by approximation of homogeneous Besov and Triebel-Lizorkin type spaces ⋮ Existence and large time behavior to coupled chemotaxis-fluid equations in Besov-Morrey spaces ⋮ Existence and large time behavior to the nematic liquid crystal equations in Besov-Morrey spaces

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Compact embeddings of radial and subradial subspaces of some Besov-type spaces related to Morrey spaces
• Fourier multipliers on Triebel-Lizorkin-type spaces
• Characterizations of Besov-type and Triebel-Lizorkin-type spaces via maximal functions and local means
• Dual properties of Triebel-Lizorkin-type spaces and their applications
• Several analytic inequalities in some \(Q\)-spaces
• Well-posedness and regularity of generalized Navier-Stokes equations in some critical \(Q\)-spaces
• A discrete transform and decompositions of distribution spaces
• Homothetic variant of fractional Sobolev space with application to Navier-Stokes system
• 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
• Generalized Navier-Stokes equations with initial data in local \(Q\)-type spaces
• Decompositions of Besov-Hausdorff and Triebel-Lizorkin-Hausdorff spaces and their applications
• Morrey and Campanato meet Besov, Lizorkin and Triebel
• Littlewood-Paley characterization for Campanato spaces
• New applications of Besov-type and Triebel-Lizorkin-type spaces
• Some new tent spaces and duality theorems for fractional Carleson measures and \(Q_{\alpha}(\mathbb R^n)\).
• Pseudodifferential operators with homogeneous symbols
• New characterizations of Besov-Triebel-Lizorkin-Hausdorff spaces including coorbits and wavelets
• Riesz transforms on \(Q\)-type spaces with application to quasi-geostrophic equation
• Local function spaces, heat and Navier-Stokes equations
• Sharp boundedness of quasiconformal composition operators on Triebel-Lizorkin type spaces
• Hausdorff Besov-type and Triebel-Lizorkin-type spaces and their applications
• Wavelets and the well-posedness of incompressible magneto-hydrodynamic equations in Besov type \(Q\)-space
• Decompositions of Besov-Morrey spaces and Triebel-Lizorkin-Morrey spaces
• A new framework for generalized Besov-type and Triebel–Lizorkin-type spaces
• COMPLEX INTERPOLATION ON BESOV-TYPE AND TRIEBEL–LIZORKIN-TYPE SPACES
• On the coincidence of certain approaches to smoothness spaces related to Morrey spaces
• Some properties of Morrey type Besov-Triebel spaces
• Modern Fourier Analysis
• CONTINUOUS CHARACTERIZATION OF THE TRIEBEL-LIZORKIN SPACES AND FOURIER MULTIPLIERS
• Biorthogonal bases of compactly supported wavelets
• Stability results on interpolation scales of quasi-Banach spaces and applications
• Semilinear heat equations and the navier-stokes equation with distributions in new function spaces as initial data
• Anisotropic Hardy spaces and wavelets
• Q spaces of several real variables
• Besov-Morrey spaces: Function space theory and applications to non-linear PDE
• Relations among Besov-type spaces, Triebel–Lizorkin-type spaces and generalized Carleson measure spaces
• The radial lemma of Strauss in the context of Morrey spaces

This page was built for publication: Function spaces of Besov-type and Triebel-Lizorkin-type -- a survey