Orlicz-Sobolev embeddings and heat kernel based Besov classes

TL;DR

This paper explores advanced functional inequalities in metric measure spaces, focusing on Besov spaces, functions of bounded variation, and their applications to isoperimetric inequalities, emphasizing local and global structural differences.

Contribution

It introduces new inequalities that account for local and global structures in metric measure spaces, especially in the context of Besov spaces and functions of bounded variation.

Findings

Development of inequalities capturing local and global space structures

Application to sets of finite perimeter and isoperimetric inequalities

Enhanced understanding of $L^1$ theory in metric measure spaces

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 $L^1$ theory and its applications to sets of finite perimeter and isoperimetric inequalities, which can now capture such structural differences.