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arXiv · 2509.04176

BMO-Interpolations and Jump Detection for Functions in $BV\cap BMO$

Paz Hashash·Arkady Poliakovsky
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Abstract

A generalization of the John--Nirenberg inequality is established. As a consequence, local and global $BMO$--interpolation inequalities in Lorentz spaces $L^{q,\gamma}$ are obtained for the full range $0<q<\infty$ and $0<\gamma\leq\infty$. These inequalities yield interpolation results in Besov spaces, fractional Sobolev spaces, and the space $BV$, including corresponding weak spaces. As a geometric application, consequences for the jump set of functions in $BV\cap BMO$ are derived.

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Paz Hashash, Arkady Poliakovsky. 2025-09-04. BMO-Interpolations and Jump Detection for Functions in $BV\cap BMO$. https://arxiv.org/abs/2509.04176

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