
Intrinsic square function characterizations of Hardy spaces associated with ball quasi-Banach function spaces
Xianjie YAN, Dachun YANG, Wen YUAN
Front. Math. China ›› 2020, Vol. 15 ›› Issue (4) : 769-806.
Intrinsic square function characterizations of Hardy spaces associated with ball quasi-Banach function spaces
Let X be a ball quasi-Banach function space satisfying some mild additional assumptions and the associated Hardy-type space. In this article, we first establish the finite atomic characterization of . As an application, we prove that the dual space of is the Campanato space associated with X. For any given and , using the atomic and the Littlewood–Paley function characterizations of ,we also establish its s-order intrinsic square function characterizations, respectively, in terms of the intrinsic Lusin-area function ,the intrinsic g-function ,and the intrinsic -function , where λ coincides with the best known range.
Ball quasi-Banach function space / Hardy space / finite atomic characterization / Campanato space / intrinsic square function
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