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

In this article, we prove interpolation results for $BMO$ in Lorentz spaces. From these results, we derive interpolation theorems in Besov spaces, the space $BV$, and fractional Sobolev spaces. As an application, we obtain geometric information about the jump set of functions in $BV \cap BMO$.

Publication Details

Journal
ArXiv.org
Published
2025-09-04
Primary Topic
Geochemistry and Geologic Mapping
Type
article
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article

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

ArXiv.org
Geochemistry and Geologic Mapping
article

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

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Abstract

In this article, we prove interpolation results for $BMO$ in Lorentz spaces. From these results, we derive interpolation theorems in Besov spaces, the space $BV$, and fractional Sobolev spaces. As an application, we obtain geometric information about the jump set of functions in $BV \cap BMO$.

ArXiv.org
Reduced inequalities
Openalex Percentile: Top 51%
Geochemistry and Geologic Mapping
Open Access PDFOpenAlex
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BMO-Interpolations and Jump Detection for Functions in $BV\cap BMO$ · ArXiv.org (2025) | TGRS Research Map | TGRS