Extension of the Best Constant Approximation Operator in Orlicz Spaces. (25th April 2020)

• Record Type: Journal Article
• Authors: Favier, Sergio; Lorenzo, Rosa
• Is Part Of: Numerical functional analysis and optimization. Volume 41:Number 6(2020)
• Page Start: 635
• Page End: 658
• Publication Date: 2020-04-25
• Subjects: Maximal inequalities -- best approximation -- Orlicz spaces; Primary: 41A10; Secondary: 41A50 -- 46E30; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2019.1666279
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: In this article we deal with the best φ -approximation operator by constants extended from an Orlicz space L φ ( Ω ) to the space L ψ + ( Ω ), where ψ + denotes the right derivative of the function φ . We obtain pointwise convergence for a suitable class of functions. Also we consider a maximal operator which allows as to get modular convergence for a specific class of Orlicz spaces.