Lebesgue-type estimates for greedy algorithms in quasi-Banach spaces

2025/08/23 by Berasategui, Miguel, Berná, Pablo M., Chu, Hung Viet +1
#46A16 #46A35 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2508.16893

Abstract

We continue the study of Lebesgue-type parameters for various greedy algorithms in quasi-Banach spaces. First, we introduce a parameter that can be used with the quasi-greedy parameter to obtain the exact growth of the Lebesgue parameter for strong partially greedy bases. Second, we establish a new upper bound for the Lebesgue parameter for semi-greedy bases using the quasi-greedy and the squeeze symmetry parameters. Finally, we answer several open questions regarding the optimal power in various bounds proved in [F. Albiac, J. L. Ansorena, and P. M. Berná, New parameters and Lebesgue-type estimates in greedy approximation, Forum Math. Sigma 10 (2022), 1-39].

Citations

• Approximation by polynomials with constant coefficients and the Thresholding Greedy Algorithm
• Linear versus nonlinear forms of partial unconditionality of bases
• Counterexamples in isometric theory of symmetric and greedy bases
• New parameters and Lebesgue-type estimates in greedy approximation
• Weak greedy algorithms and the equivalence between semi-greedy and almost greedy Markushevich bases
• A note on partially-greedy bases in quasi-Banach spaces
• Strong partially greedy bases and Lebesgue-type inequalities
• Greedy approximation for biorthogonal systems in quasi-Banach spaces
• Characterization of weight-semi-greedy bases
• Lebesgue inequalities for Chebyshev Thresholding Greedy Algorithms
• Equivalence between almost-greedy and semi-greedy bases
• The weighted Property (A) and the greedy algorithm
• Embeddings and Lebesgue-type inequalities for the greedy algorithm in Banach spaces
• Lebesgue inequalities for the greedy algorithm in general bases
• Characterization of 1-almost greedy bases
• Lebesgue-Type inequalities for quasi-greedy bases

Related

• New parameters and Lebesgue-type estimates in greedy approximation
• Lebesgue inequalities for the greedy algorithm in general bases
• Lebesgue-Type inequalities for quasi-greedy bases
• Strong partially greedy bases and Lebesgue-type inequalities
• Lebesgue type inequalities for quasi-greedy bases