The Weak Chebyshev Greedy Algorithm (WCGA) in L^p (log L)^α spaces

2022/09/12 by Gustavo Garrigós, Garrigós, Gustavo
Engineering · Mathematics · #Sparse and Compressive Sensing Techniques #Mathematical Approximation and Integration #Advanced Harmonic Analysis Research

paper · pdf · doi:10.48550/arxiv.2209.05404

Abstract

We present some new results concerning Lebesgue-type inequalities for the Weak Chebyshev Greedy Algorithm (WCGA) in uniformly smooth Banach spaces \mathbbX. First, we generalize a result of Temlyakov to cover situations in which the modulus of smoothness and the so called A3 parameter are not necessarily power functions. Secondly, we apply this new theorem to the Zygmund spaces \mathbbX=L^p(log L)^α, with 10, takes the form ϕ(N)≈ log(log N).

Related

• Lebesgue-type inequalities in greedy approximation
• Lebesgue inequalities for Chebyshev Thresholding Greedy Algorithms
• Sparse approximation and recovery by greedy algorithms in Banach spaces
• Lebesgue inequalities for the greedy algorithm in general bases
• Lebesgue-type estimates for greedy algorithms in quasi-Banach spaces