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

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. Bern\'a, New parameters and Lebesgue-type estimates in greedy approximation, Forum Math. Sigma 10 (2022), 1-39].