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- W2979544057 abstract "Let X be a ball quasi-Banach function space on $${mathbb R}^n$$ . In this article, assuming that the powered Hardy–Littlewood maximal operator satisfies some Fefferman–Stein vector-valued maximal inequality on X as well as it is bounded on both the weak ball quasi-Banach function space WX and the associated space, the authors establish various Littlewood–Paley function characterizations of $$WH_X({{mathbb {R}}}^n)$$ under some weak assumptions on the Littlewood–Paley functions. The authors also prove that the real interpolation intermediate space $$(H_{X}({{mathbb {R}}}^n),L^infty ({{mathbb {R}}}^n))_{theta ,infty }$$ , between the Hardy space associated with X, $$H_{X}({{mathbb {R}}}^n)$$ , and the Lebesgue space $$L^infty ({mathbb R}^n)$$ , is $$WH_{X^{{1}/{(1-theta )}}}({{mathbb {R}}}^n)$$ , where $$theta in (0, 1)$$ . All these results are of wide applications. Particularly, when $$X:=M_q^p({{mathbb {R}}}^n)$$ (the Morrey space), $$X:=L^{vec {p}}({{mathbb {R}}}^n)$$ (the mixed-norm Lebesgue space) and $$X:=(E_Phi ^q)_t({{mathbb {R}}}^n)$$ (the Orlicz-slice space), all these results are even new; when $$X:=L_omega ^Phi ({mathbb R}^n)$$ (the weighted Orlicz space), the result on the real interpolation is new and, when $$X:=L^{p(cdot )}({{mathbb {R}}}^n)$$ (the variable Lebesgue space) and $$X:=L_omega ^Phi ({{mathbb {R}}}^n)$$ , the Littlewood–Paley function characterizations of $$WH_X({{mathbb {R}}}^n)$$ obtained in this article improves the existing results via weakening the assumptions on the Littlewood–Paley functions." @default.
- W2979544057 created "2019-10-18" @default.
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- W2979544057 date "2019-10-12" @default.
- W2979544057 modified "2023-10-17" @default.
- W2979544057 title "Weak Hardy-Type Spaces Associated with Ball Quasi-Banach Function Spaces II: Littlewood–Paley Characterizations and Real Interpolation" @default.
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- W2979544057 doi "https://doi.org/10.1007/s12220-019-00293-1" @default.
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