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• W3044516084 endingPage "105459" @default.
• W3044516084 startingPage "105459" @default.
• W3044516084 abstract "Let S(Rn) be the Schwartz class on Rn and S∞(Rn)≔ϕ∈S(Rn):∫Rnxαϕ(x)dx=0for any multi-indexα∈({0,1,…})n,and S′(Rn) and S∞′(Rn) be their dual spaces, respectively. Let a→≔(a1,…,an)∈[1,∞)n, p→≔(p1,…,pn)∈(0,1]n, and Ha→p→(Rn)⊂S′(Rn) be the anisotropic mixed-norm Hardy space, associated with an anisotropic quasi-homogeneous norm |⋅|a→, defined via the non-tangential grand maximal function. In this article, via the known atomic characterizations and Lusin area function characterizations of Ha→p→(Rn), the authors first establish a new atomic characterization of Ha→p→(Rn) in terms of S∞′(Rn). Applying this atomic characterization, the authors then obtain the Littlewood–Paley g-function characterization of Ha→p→(Rn) in terms of S∞′(Rn), which further induces the identification of Ha→p→(Rn) and certain anisotropic homogeneous mixed-norm Triebel–Lizorkin spaces. As applications, the authors obtain the dual theorem on some anisotropic homogeneous mixed-norm Triebel–Lizorkin spaces and the boundedness of Fourier multipliers as well as anisotropic pseudo-differential operators on Ha→p→(Rn). All these results are new even for isotropic mixed-norm Hardy spaces on Rn." @default.
• W3044516084 created "2020-07-29" @default.
• W3044516084 creator A5068607724 @default.
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• W3044516084 date "2020-10-01" @default.
• W3044516084 modified "2023-10-15" @default.
• W3044516084 title "Identification of anisotropic mixed-norm Hardy spaces and certain homogeneous Triebel–Lizorkin spaces" @default.
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• W3044516084 doi "https://doi.org/10.1016/j.jat.2020.105459" @default.
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