Spectra of Generalized Bochner–Riesz Means on Weighted Spaces. (27th July 2019)

• Record Type: Journal Article
• Authors: Fang, Qiquan; Tao, Xiangxing
• Is Part Of: Numerical functional analysis and optimization. Volume 40:Number 10(2019)
• Page Start: 1136
• Page End: 1149
• Publication Date: 2019-07-27
• Subjects: Generalized Bochner–Riesz means -- spectral invariance -- weighted Lp -- Wiener's lemma; 47L80 -- 42B20; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2019.1578793
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: In this paper, we introduce a family of generalized Bochner–Riesz means and show that their spectra on weighted L p spaces, 1 ≤ p < ∞, are either the whole complex plane or the interval [ 0, a ] for some a ≥ 0 . Also we extend the above spectral property to weighted Triebel–Lizorkin spaces, weighted Besov spaces, and weighted Herz spaces.