Lower bounds for Haar projections: deterministic examples

DOI10.1007/s00365-016-9353-3zbMath1386.46037arXiv1511.01470OpenAlexW2592744506MaRDI QIDQ1675127

Tino Ullrich, Andreas Seeger

Publication date: 26 October 2017

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

Full work available at URL: https://arxiv.org/abs/1511.01470

zbMATH Keywords

Sobolev spacesTriebel-Lizorkin spacesBesov spacesHaar systemunconditional bases

Mathematics Subject Classification ID

Nontrigonometric harmonic analysis involving wavelets and other special systems (42C40) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces (46B15)

Related Items (12)

Orthogonal systems of spline wavelets as unconditional bases in Sobolev spaces ⋮ Haar frame characterizations of Besov-Sobolev spaces and optimal embeddings into their dyadic counterparts ⋮ Embeddings and characterizations of Lipschitz spaces ⋮ The Haar system in Besov-type spaces ⋮ On uniform boundedness of dyadic averaging operators in spaces of Hardy-Sobolev type ⋮ Haar projection numbers and failure of unconditional convergence in Sobolev spaces ⋮ The Haar system as a Schauder basis in spaces of Hardy-Sobolev type ⋮ The Role of Frolov's Cubature Formula for Functions with Bounded Mixed Derivative ⋮ The Haar system in Triebel-Lizorkin spaces: endpoint results ⋮ Multivariate Haar systems in Besov function spaces ⋮ A higher order Faber spline basis for sampling discretization of functions ⋮ Basis Properties of the Haar System in Limiting Besov Spaces

Cites Work

• Haar projection numbers and failure of unconditional convergence in Sobolev spaces
• Bases in function spaces, sampling, discrepancy, numerical integration
• Theory of function spaces II
• The Haar system as a Schauder basis in spaces of Hardy-Sobolev type
• Greedy Approximation
• CONVOLUTION OPERATORS ON BANACH SPACE VALUED FUNCTIONS
• NECESSARY CONDITIONS FOR VECTOR-VALUED OPERATOR INEQUALITIES IN HARMONIC ANALYSIS
• Über die Existenz von Schauderbasen in Sobolev-Besov-Räumen. Isomorphiebeziehungen
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