Product Besov and Triebel-Lizorkin spaces with application to nonlinear approximation

DOI10.1007/s00365-019-09490-1zbMath1460.42026OpenAlexW2997077424WikidataQ126526089 ScholiaQ126526089MaRDI QIDQ2658523

Athanasios G. Georgiadis, George C. Kyriazis, Pencho P. Petrushev

Publication date: 23 March 2021

Published in: Constructive Approximation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00365-019-09490-1

zbMATH Keywords

waveletsTriebel-Lizorkin spacesBesov spacesnonlinear approximationproduct spacesBernstein estimateJackson estimate\( \varphi \)-transform

Mathematics Subject Classification ID

Nontrigonometric harmonic analysis involving wavelets and other special systems (42C40) Maximal functions, Littlewood-Paley theory (42B25) Function spaces arising in harmonic analysis (42B35) Operations with distributions and generalized functions (46F10) Inequalities in approximation (Bernstein, Jackson, Nikol'ski?-type inequalities) (41A17)

Related Items (3)

Product \((\alpha_1, \alpha_2)\)-modulation spaces ⋮ Anisotropic ball Campanato-type function spaces and their applications ⋮ Fourier Transform of Anisotropic Mixed-norm Hardy Spaces with Applications to Hardy-Littlewood Inequalities

Cites Work

• Anisotropic singular integrals in product spaces
• A discrete transform and decompositions of distribution spaces
• Decomposition of Besov and Triebel-Lizorkin spaces on the sphere
• Theory of function spaces
• Harmonic analysis on product spaces
• Hyperbolic wavelet approximation
• Singular integrals on product \(H^ p\) spaces
• Restricted nonlinear approximation
• Littlewood-Paley characterization and duality of weighted anisotropic product Hardy spaces
• New bases for Triebel-Lizorkin and Besov spaces
• Some recent developments in Fourier analysis and 𝐻^{𝑝}-theory on product domains
• Weighted anisotropic product Hardy spaces and boundedness of sublinear operators
• Ten Lectures on Wavelets
• Biorthogonal bases of compactly supported wavelets
• H ^p theory for the poly-disc
• Function spaces with dominating mixed smoothness
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