# Classic and exotic Besov spaces induced by good grids

## TL;DR

This paper explores Besov spaces defined via good grids, showing classical spaces are special cases and introducing exotic variants that differ from classical definitions.

## Contribution

It demonstrates that classical Besov spaces on compact homogeneous spaces are examples of Besov spaces induced by good grids, and introduces exotic Besov spaces from interval partitions.

## Key findings

- Classical Besov spaces are special cases of good grid-induced Besov spaces.
- Exotic Besov spaces can differ from classical ones when defined by interval partitions.
- The framework unifies and extends the understanding of Besov spaces on various measure spaces.

## Abstract

In a previous work we introduced Besov spaces $\mathcal{B}^s_{p,q}$ defined on a measure spaces with a good grid, with $p\in [1,\infty)$, $q\in [1,\infty]$ and $0< s< 1/p$. Here we show that classical Besov spaces on compact homogeneous spaces are examples of such Besov spaces. On the other hand we show that even Besov spaces defined by a good grid made of partitions by intervals may differ from a classical Besov space, giving birth to exotic Besov spaces.