Discrete decomposition of homogeneous mixed-norm Besov spaces

DOI10.1090/conm/693/13931zbMath1388.42056OpenAlexW4241685833MaRDI QIDQ4635384

Athanasios G. Georgiadis, Galatia Cleanthous, Morten Nielsen

Publication date: 16 April 2018

Published in: Functional Analysis, Harmonic Analysis, and Image Processing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/conm/693/13931

zbMATH Keywords

\(\phi\)-transformdiscrete decomposition transformationinhomogeneous mixed-norm Besov spaces

Mathematics Subject Classification ID

Maximal functions, Littlewood-Paley theory (42B25) Function spaces arising in harmonic analysis (42B35) Operations with distributions and generalized functions (46F10)

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Cites Work

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• On the Hörmander-Mihlin theorem for mixed-norm Lebesgue spaces
• Homogeneous Besov and Triebel-Lizorkin spaces associated to non-negative self-adjoint operators
• Leibniz's rule, sampling and wavelets on mixed Lebesgue spaces
• A discrete transform and decompositions of distribution spaces
• The spaces \(L^ p\), with mixed norm
• On the construction of frames for spaces of distributions
• Decomposition of Besov and Triebel-Lizorkin spaces on the sphere
• On anisotropic Triebel-Lizorkin type spaces, with applications to the study of pseudo-differential operators
• Theory of function spaces
• Theory of function spaces II
• Vector-valued singular integral operators on \(L^ p\)-spaces with mixed norms and applications
• New characterizations of Besov-Triebel-Lizorkin-Hausdorff spaces including coorbits and wavelets
• Heat kernel generated frames in the setting of Dirichlet spaces
• A direct proof of Sobolev embeddings for quasi-homogeneous Lizorkin-Triebel spaces with mixed norms
• Atomic and molecular decompositions of anisotropic Besov spaces
• Localized polynomial frames on the interval with Jacobi weights
• New bases for Triebel-Lizorkin and Besov spaces
• Pseudodifferential operators on mixed-norm Besov and Triebel-Lizorkin spaces
• Decomposition of weighted Triebel-Lizorkin and Besov spaces on the ball
• Ten Lectures on Wavelets
• An Extended Inequality for the Maximal Function
• Decomposition systems for function spaces
• Isotropic and dominating mixed Besov spaces: A comparison
• On the trace problem for Lizorkin–Triebel spaces with mixed norms
• Rational bases for spaces of holomorphic functions in the disc
• Heat kernel based decomposition of spaces of distributions in the framework of Dirichlet spaces
• Atomic and molecular decompositions of anisotropic Triebel-Lizorkin spaces