Bochner–Riesz Means and K-Functional on Triebel–Lizorkin Spaces. (17th February 2022)

• Record Type: Journal Article
• Authors: Chen, Jiecheng; Fan, Dashan; Zhao, Fayou
• Is Part Of: Numerical functional analysis and optimization. Volume 43:Number 3(2022)
• Page Start: 273
• Page End: 306
• Publication Date: 2022-02-17
• Subjects: Bochner–Riesz means -- homogeneous Triebel–Lizorkin spaces -- norm convergence; 47A58 -- 41A25 -- 42B35 -- 42B15; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2022.2026957
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: Based on n -dimensional Euclidean spaces and n -dimensional torus as underlying spaces, we investigate the rate for the norm convergence of the generalized Bochner–Riesz means on homogeneous Triebel–Lizorkin spaces, and establish the equivalence between the rate and the K -functional. Particularly, we show that such equivalence is closely related to the Bochner–Riesz conjecture on homogeneous Triebel–Lizorkin spaces. Thus, we obtain natural extensions of some well-known theorems by Fefferman, Tomas and Stein and by Carleson, Söjlin and Hörmander.