Orlicz-Sobolev embeddings and heat kernel based Besov classes

Q: What type of study is this?

This is a Quantitative Study study.

Patricia Alonso Ruiz; Fabrice Baudoin

doi:10.48550/arxiv.2505.09212

May 14, 2025Open Access

Orlicz-Sobolev embeddings and heat kernel based Besov classes

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Key Points

Functional inequalities in Besov spaces show significant effects on isoperimetric inequalities, influencing structural understanding.
Key results involve $L^1$ theory and its application to sets of finite perimeter, illustrating necessary relationships.
By examining metric measure spaces, the research offers new insights into bounded variation and the underlying local structures.
The findings hold potential implications for functional analysis and metric geometry, suggesting avenues for further exploration.

Implication

This analysis reveals structural differences in Besov spaces on metric measure spaces, highlighting implications for bounded variation.

Abstract

This paper investigates functional inequalities involving Besov spaces and functions of bounded variation, when the underlying metric measure space displays different local and global structures. Particular focus is put on the L¹ theory and its applications to sets of finite perimeter and isoperimetric inequalities, which can now capture such structural differences.

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Cite This Study

Ruiz et al. (2025) studied this question.

synapsesocial.com/papers/68e82b12e7fc21a30050043c https://doi.org/10.48550/arxiv.2505.09212

View Full Paper

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Orlicz-Sobolev embeddings and heat kernel based Besov classes

Key Points

Implication

Abstract

Discussion

Cite This Study

Orlicz-Sobolev embeddings and heat kernel based Besov classes

Key Points

Implication

Abstract

Discussion

Cite This Study

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