Democracy functions and optimal embeddings for approximation spaces

2009/11/25 by Gustavo Garrigós, Garrigós, Gustavo, Eugenio Hernández +3
Mathematics · #41A17 #42C40 #Advanced Harmonic Analysis Research #Approximation Theory and Sequence Spaces #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.0911.4900

openalex publication_date 2009/11/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We prove optimal embeddings for nonlinear approximation spaces in terms of weighted Lorentz sequence spaces, with the weights depending on the democracy functions of the basis. As applications we recover known embeddings for N-term wavelet approximation in Lebesgue, Orlicz, and Lorentz norms. We also study the "greedy classes" introduced by Gribonval and Nielsen.

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