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.

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PDF(464 KB)
Front. Math. China ›› 2020, Vol. 15 ›› Issue (4) : 769-806. DOI: 10.1007/s11464-020-0849-6
RESEARCH ARTICLE
RESEARCH ARTICLE

Intrinsic square function characterizations of Hardy spaces associated with ball quasi-Banach function spaces

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Abstract

Let X be a ball quasi-Banach function space satisfying some mild additional assumptions and HX(n) the associated Hardy-type space. In this article, we first establish the finite atomic characterization of HX(n). As an application, we prove that the dual space of HX(n) is the Campanato space associated with X. For any given α(0,1] and s+, using the atomic and the Littlewood–Paley function characterizations of HX(n),we also establish its s-order intrinsic square function characterizations, respectively, in terms of the intrinsic Lusin-area function Sα,s,the intrinsic g-function gα,s,and the intrinsic gλ-function gλ,α,s, where λ coincides with the best known range.

Keywords

Ball quasi-Banach function space / Hardy space / finite atomic characterization / Campanato space / intrinsic square function

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Xianjie YAN, Dachun YANG, Wen YUAN. Intrinsic square function characterizations of Hardy spaces associated with ball quasi-Banach function spaces. Front. Math. China, 2020, 15(4): 769‒806 https://doi.org/10.1007/s11464-020-0849-6

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