Orlicz-Sobolev embeddings and heat kernel based Besov classes

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.