Favier, Sergio; Zó, Felipe A Lebesgue type differentiation theorem for best approximations by constants in Orlicz spaces. (English) Zbl 1068.41047 Real Anal. Exch. 30(2004-2005), No. 1, 29-42 (2005). The authors extend the best approximation operator by constants from an Orlicz space to the class of all Lebesgue measurable functions. Weak and strong inequalities are established for the maximal functions. Reviewer: Hang Tong Lau (Montréal) Cited in 9 Documents MSC: 41A50 Best approximation, Chebyshev systems 42B25 Maximal functions, Littlewood-Paley theory 46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) Keywords:Orlicz spaces; best approximations; maximal functions; convergence PDFBibTeX XMLCite \textit{S. Favier} and \textit{F. Zó}, Real Anal. Exch. 30, No. 1, 29--42 (2005; Zbl 1068.41047) Full Text: DOI