BMO Functions Generated by AXℝn Weights on Ball Banach Function Spaces. (8th January 2021)

• Record Type: Journal Article
• Authors: Wu, Ruimin; Wang, Songbai
• Other Names: Ana Maria Acu Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2021(2021)
• Publication Date: 2021-01-08
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2021/6626787
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : Let X be a ball Banach function space on ℝ n . We introduce the class of weights A X ℝ n . Assuming that the Hardy-Littlewood maximal function M is bounded on X and X ′, we obtain that BMO ℝ n = α ln ω : α ≥ 0, ω ∈ A X ℝ n . As a consequence, we have BMO ℝ n = α ln ω : α ≥ 0, ω ∈ A L p · ℝ n ℝ n, where L p · ℝ n is the variable exponent Lebesgue space. As an application, if a linear operator T is bounded on the weighted ball Banach function space X ω for any ω ∈ A X ℝ n, then the commutator b, T is bounded on X with b ∈ BMO ℝ n .