BMO Functions Generated by AXℝn Weights on Ball Banach Function Spaces. (8th January 2021) - Wu, Ruimin; Wang, Songbai
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 .