Wavelets and local Triebel–Lizorkin spaces with the Lorentz index. (18th October 2018)

• Record Type: Journal Article
• Authors: Yang, Qixiang; Wang, Hua
• Is Part Of: Mathematical methods in the applied sciences. Volume 42:Number 1(2019)
• Page Start: 237
• Page End: 249
• Publication Date: 2018-10-18
• Subjects: local norm -- oscillation -- Triebel–Lizorkin–Lorentz–Morrey spaces -- wavelets; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.5339
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : In this paper, we apply wavelets to consider local norm function spaces with the Lorentz index. Triebel–Lizorkin–Lorentz spaces are based on the real interpolation of the Triebel–Lizorkin spaces. Triebel–Lizorkin–Morrey spaces are based on local norm of the Triebel–Lizorkin spaces. We give a unified depict of spaces that include these two kinds of spaces. Each index of the five index spaces represents a property of functions. We prove the wavelet characterization of the Triebel–Lizorkin–Lorentz–Morrey spaces and use such characterization to study some basic properties of these spaces.