2021/08/03 by Hongchao Jia, Jia, Hongchao, Dachun Yang +5
Mathematics · #42B30 #42B35 #46E35 #47A30 #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 #Primary 42B25 #Secondary 42B20
paper · pdf · doi:10.48550/arxiv.2108.01559
openalex publication_date 2021/08/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let X be a ball quasi-Banach function space on \mathbb Rn and assume that the Hardy--Littlewood maximal operator satisfies the Fefferman--Stein vector-valued maximal inequality on X, and let q∈[1,∞) and d∈(0,∞). In this article, the authors prove that, for any f∈ LX,q,0,d(ℝn) (the ball Campanato-type function space associated with X), the Littlewood--Paley g-function g(f) is either infinite everywhere or finite almost everywhere and, in the latter case, g(f) is bounded on LX,q,0,d(ℝn). Similar results for both the Lusin-area function and the Littlewood--Paley gλ^*-function are also obtained. All these results have a wide range of applications. Particularly, even when X is the weighted Lebesgue space, or the mixed-norm Lebesgue space, or the variable Lebesgue space, or the Orlicz space, or the Orlicz-slice space, all these results are new. The proofs of all these results strongly depend on several delicate estimates of Littlewood--Paley operators on the mean oscillation of the locally integrable function f on ℝn. Moreover, the same ideas are also used to obtain the corresponding results for the special John--Nirenberg--Campanato space via congruent cubes.