发表机构
University of Zagreb（萨格勒布大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文为紧支撑BMO函数建立以支撑集Lebesgue测度替代直径的尖锐局部$L^r$界，并应用于几何坍缩、薛定谔算子谱界及奇异积分解耦。
AI 中文摘要
我们为紧支撑的有界平均振荡（BMO）函数建立了尖锐的局部$L^r$界。通过John-Nirenberg不等式得到的经典估计用该函数支撑集的直径来界定其$L^r$范数。我们证明，直径依赖性可以被支撑集的Lebesgue测度所替代，这对于薄且高度偏心的域是相关的量。证明依赖于非递增重排和Bennett-DeVore-Sharpley定理，并且不需要消失振荡假设。我们给出了物理和算子理论方面的应用：管状邻域中的几何坍缩、薛定谔算子的局部Cwikel-Lieb-Rozenblum界，以及Calderón-Zygmund奇异积分局部作用的解耦界。
英文摘要
We establish sharp localized $L^r$ bounds for compactly supported functions of bounded mean oscillation (BMO). Classical estimates obtained via the John-Nirenberg inequality bound the $L^r$ norm of such a function in terms of the diameter of its support. We show that the diameter dependence can be replaced by the Lebesgue measure of the support, the relevant quantity for thin, highly eccentric domains. The proof relies on non-increasing rearrangements and the Bennett-DeVore-Sharpley theorem, and requires no vanishing-oscillation hypothesis. We present physical and operator-theoretic applications: geometric collapse in tubular neighborhoods, a localized Cwikel-Lieb-Rozenblum bound for Schrödinger operators, and decoupling bounds for the localized action of Calderón-Zygmund singular integrals.
CommentsWork in progress
