Inequalities for the extended best polynomial approximation operator in Orlicz spaces

ACINAS, SONIA; FAVIER, SERGIO; ZÓ, FELIPE

ACTA MATHEMATICA SINICA-ENGLISH SERIES

SPRINGER HEIDELBERG

Lugar: HEIDELBERG; Año: 2019 vol. 35 p. 185 - 203

1439-8516

In this paper we pursue the study of the best approximation operator extended from LΦ to Lφ, where φ denotes the derivative of the function Φ. We get pointwise convergence for the coefficients of the extended best approximation polynomials for a wide class of function f, closely related to the Calderón-Zygmund class tp m(x) which had been introduced in 1961. We also obtain weak and strong type inequalities for a maximal operator related to the extended best polynomial approximation and a norm convergence result for the coefficients is derived. In most of these results, we have to consider Matuszewska-Orlicz indices for the function φ.