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Wavelets and local Triebel–Lizorkin spaces with the Lorentz index
Author(s) -
Yang Qixiang,
Wang Hua
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5339
Subject(s) - mathematics , interpolation space , lorentz transformation , birnbaum–orlicz space , characterization (materials science) , lorentz space , wavelet , norm (philosophy) , pure mathematics , topological tensor product , lp space , function space , index (typography) , hardy space , mathematical analysis , functional analysis , computer science , artificial intelligence , banach space , political science , biochemistry , chemistry , physics , classical mechanics , world wide web , law , gene , materials science , nanotechnology
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.