| 1 | Inequalities for the Extended Best Polynomial Approximation Operator in Orlicz Spaces显示文摘In this paper we pursue the study of the best approximation operator extended from L~Φ to L~φ, 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 Calder′on–Zygmund class t_m^p(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. | Sonia ACINAS Sergio FAVIER Felipe ZO | 2019 | Acta Mathematica Sinica,English Series2019，35，2： | 0 |
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