arXiv subjects

Sergio Favier

Publications and source records attributed to Sergio Favier.

4 recordsLinked to original sources

arXiv2026

The best Musielak-Orlicz approximation by linear subspaces

We study best modular approximation in Musielak-Orlicz spaces. A geometric classification near the origin of Orlicz functions is introduced to isolate weighted $L^1$-like behavior. We establish existence results under minimal hypotheses and provide a variational characterization of minimizers via lateral derivatives. Finally, we establish uniqueness criteria, including a one-dimensional Haar-type theorem and characterizations in $0$- and $1$-spaces in higher dimensions.

math.FA↗

arXiv2026

On the Uniqueness of Best Non-decreasing Approximation in Orlicz Spaces

Given an approximately continuous function $f$ in an Orlicz space $L^Φ([a,b]),$ for a suitable class of convex functions $Φ,$ we employ a characterization of the best monotone approximation set to establish its continuity, which in turn yields the uniqueness property for the best monotone approximation in $L^Φ([a,b]).$

math.FA↗

arXiv2025

Extension of the Best Polynomial Operator in Generalized Orlicz spaces

In this paper, we consider the best multivalued polynomial approximation operator for functions in an Orlicz Space $L^φ(Ω)$. We obtain its characterization involving $ψ^-$ and $ψ^+$, which are the left and right derivatives functions of $φ$. And then, we extend the operator to $L^{ψ^+}(Ω)$. We also get pointwise convergence of this extension, where the Calderón-Zygmund class $t_m^p (x)$ adapted to $L^{ψ^+}(Ω)$ plays an important role.

math.CA↗

arXiv2024

On the uniqueness of best approximation in Orlicz spaces

We study uniqueness of best approximation in Orlicz spaces L$Φ$, for different types of convex functions $Φ$ and for some finite dimensional approximation classes of functions, where Tchebycheff spaces, and more general approximation ones, are involved

math.FA↗