Albiac Alesanco, Fernando JoséAnsorena, José L.Berná, Pablo M.2023-04-042023-04-042022Albiac, F., Ansorena, J. L., Berná, P. M. (2022) New parameters and Lebesgue-type estimates in greedy approximation. Forum of Mathematics, Sigma, 10, 1-39. https://doi.org/10.1017/fms.2022.102.2050-509410.1017/fms.2022.102https://academica-e.unavarra.es/handle/2454/45056The purpose of this paper is to quantify the size of the Lebesgue constants (𝑳𝑚)∞ 𝑚=1 associated with the thresholding greedy algorithm in terms of a new generation of parameters that modulate accurately some features of a general basis. This fine tuning of constants allows us to provide an answer to the question raised by Temlyakov in 2011 to find a natural sequence of greedy-type parameters for arbitrary bases in Banach (or quasi-Banach) spaces which combined linearly with the sequence of unconditionality parameters (𝒌𝑚)∞ 𝑚=1 determines the growth of (𝑳𝑚)∞ 𝑚=1. Multiple theoretical applications and computational examples complement our study.application/pdfeng© The Author(s), 2022. This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence.Lebesgue constantsGreedy approximationArtículo / Artikulua2023-04-04Acceso abierto / Sarbide irekiainfo:eu-repo/semantics/openAccess