Lebesgue-type inequalities for quasi-greedy bases

DOI10.1007/s00365-013-9209-zzbMath1284.41023arXiv1207.0946OpenAlexW1967146357MaRDI QIDQ387546

Eugenio Hernández, Gustavo Garrigós, Timur Oikhberg

Publication date: 23 December 2013

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

Full work available at URL: https://arxiv.org/abs/1207.0946

zbMATH Keywords

bounded variationnonlinear approximationquasi-greedy basesdemocracy functionsLebesgue-type inequalitiesthresholding greedy algorithm

Mathematics Subject Classification ID

Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) (41A65) Inequalities in approximation (Bernstein, Jackson, Nikol'ski?-type inequalities) (41A17) Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces (46B15) Approximation by arbitrary nonlinear expressions; widths and entropy (41A46)

Related Items (25)

Embeddings and Lebesgue-type inequalities for the greedy algorithm in Banach spaces ⋮ Lorentz spaces and embeddings induced by almost greedy bases in Banach spaces ⋮ Lebesgue constants for Chebyshev thresholding greedy algorithms ⋮ Lebesgue-type inequalities in greedy approximation ⋮ Efficiency of weak greedy algorithms for \(m\)-term approximations ⋮ New parameters and Lebesgue-type estimates in greedy approximation ⋮ Lebesgue inequalities for the greedy algorithm in general bases ⋮ Weak forms of unconditionality of bases in greedy approximation ⋮ Asymptotic greediness of the Haar system in the spaces \(L_p[0,1\), \(1<p<\infty \)] ⋮ Characterization of 1-quasi-greedy bases ⋮ Weight-almost greedy bases ⋮ Fourier coefficients of functions in power-weighted L₂-spaces and conditionality constants of bases in Banach spaces ⋮ Lorentz spaces and embeddings induced by almost greedy bases in superreflexive Banach spaces ⋮ Lebesgue inequalities for Chebyshev thresholding greedy algorithms ⋮ Sparse Approximation by Greedy Algorithms ⋮ Bidemocratic bases and their connections with other greedy-type bases ⋮ Building highly conditional almost greedy and quasi-greedy bases in Banach spaces ⋮ Quasi-greedy bases in \(\ell_p\) (\(0 < p < 1\)) are democratic ⋮ On certain subspaces of \(\ell_p\) for \(0 < p \le 1\) and their applications to conditional quasi-greedy bases in \(p\)-Banach spaces ⋮ Conditional quasi-greedy bases in non-superreflexive Banach spaces ⋮ Equivalence between almost-greedy and semi-greedy bases ⋮ Strong partially greedy bases and Lebesgue-type inequalities ⋮ Greedy approximation for biorthogonal systems in quasi-Banach spaces ⋮ Variations of property (A) constants and Lebesgue-type inequalities for the weak thresholding greedy algorithms ⋮ Lebesgue constants for the weak greedy algorithm

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