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arXiv · 2209.05404

The Weak Chebyshev Greedy Algorithm (WCGA) in $L^p (\log L)^\alpha$ spaces

Gustavo Garrigós
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Abstract

We present some new results concerning Lebesgue-type inequalities for the Weak Chebyshev Greedy Algorithm (WCGA) in uniformly smooth Banach spaces $\mathbb{X}$. 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 $\mathbb{X}=L^p(\log L)^\alpha$, with $1 0$, takes the form $\phi(N)\approx \log(\log N)$.

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Gustavo Garrigós. 2022-09-12. The Weak Chebyshev Greedy Algorithm (WCGA) in $L^p (\log L)^\alpha$ spaces. https://arxiv.org/abs/2209.05404

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