A new concept of smoothness in Orlicz spaces
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Ferreyra, D. E. [1]
;
Levis, F. E.
[1]
;
Roldán, M. V.
[2]
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[1] Universidad Nacional de Río Cuarto
Universidad Nacional de Río Cuarto
Argentina
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[2] Universidad Nacional de La Pampa
Universidad Nacional de La Pampa
Argentina
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- Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 73, Fasc. 3, 2022, págs. 505-520
- Idioma: inglés
- DOI: 10.1007/s13348-021-00331-8
- Texto completo no disponible (Saber más ...)
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Resumen
In a 2015 article Cuenya and Ferreyra defined a class of functions in L^p-spaces, denoted by c_n^p(x). The class c_n^p(x) contains the class of L^p-differentiability functions, denoted by t_n^p(x), introduced in a 1961 article by Calderón-Zygmund. A more recent paper by Acinas, Favier and Zó introduced a new class of functions in Orlicz spaces L^\Phi, called L^\Phi-differentiable functions in the present article. The class of L^\Phi-differentiable functions is closely related to the class t_n^p(x). In this work, we define a class of functions in L^\Phi, denoted by c_n^{\Phi }(x). The class c_n^{\Phi }(x) is more general than the class of L^{\varPhi}-differentiable functions. We prove the existence of the best local \Phi-approximation for functions in c_n^{\varPhi }(x) and study the convexity of the set of cluster points of the set of best \Phi-approximations to a function on an interval when their measures tend to zero.
