2019/11/09 by Der‐Chen Chang, Songbai Wang, Chang, Der-Chen +5 · 1 citation
Mathematics · #42B25 (Primary) #42B30 #42B35 #46E30 (Secondary) #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Partial Differential Equations
paper · pdf · doi:10.48550/arxiv.1911.04953
openalex publication_date 2019/11/09 · openalex created_date 2019/11/22 · openalex updated_date 2026/07/28
Let X be a ball quasi-Banach function space on \mathbb Rn. In this article, assuming that the powered Hardy--Littlewood maximal operator satisfies some Fefferman--Stein vector-valued maximal inequality on X and is bounded on the associated space, the authors establish various Littlewood--Paley function characterizations of the Hardy space HX(\mathbb Rn) associated with X, under some weak assumptions on the Littlewood--Paley functions. To this end, the authors also establish a useful estimate on the change of angles in tent spaces associated with X. All these results have wide applications. Particularly, when X:=Mrp(\mathbb Rn) (the Morrey space), X:=L^p(\mathbb Rn) (the mixed-norm Lebesgue space), X:=Lp(⋅)(\mathbb Rn) (the variable Lebesgue space), X:=Lωp(\mathbb Rn) (the weighted Lebesgue space) and X:=(EΦr)t(\mathbb Rn) (the Orlicz-slice space), the Littlewood--Paley function characterizations of HX(\mathbb Rn) obtained in this article improve the existing results via weakening the assumptions on the Littlewood--Paley functions and widening the range of λ in the Littlewood--Paley gλ^*-function characterization of HX(\mathbb Rn).