info:eu-repo/semantics/article
A new concept of smoothness in Orlicz spaces
Fecha
2021-09-17Registro en:
Ferreyra, David Eduardo; Levis, Fabián Eduardo; Roldán, Marina Vanesa; A new concept of smoothness in Orlicz spaces; Universidad de Barcelona; Collectanea Mathematica; 2021; 17-9-2021; 1-16
0010-0757
2038-4815
CONICET Digital
CONICET
Autor
Ferreyra, David Eduardo
Levis, Fabián Eduardo
Roldán, Marina Vanesa
Resumen
In a 2015 article Cuenya and Ferreyra defined a class of functions in Lp-spaces, denoted by cpn(x). The class cpn(x) contains the class of Lp -differentiability functions, denoted by tpn(x), introduced in a 1961 article by Calderón-Zygmun. A more recent paper by Acinas, Favier and Zó introduced a new class of functions in Orlicz spaces LΦ, called L Φ-differentiable functions in the present article. The class of LΦ-differentiable functions is closely related to the class tpn(x). In this work, we define a class of functions in LΦ, denoted by cΦn(x). The class cΦn(x) is more general than the class of LΦ-differentiable functions. We prove the existence of the best local Φ-approximation for functions in cΦn(x) and study the convexity of the set of cluster points of the set of best Φ-approximations to a function on an interval when their measures tend to zero.