Classic and exotic Besov spaces induced by good grids

Abstract

In a previous work we introduced Besov spaces ${\mathcal{B}}_{p,q}^s$ 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.

35 pages, 1 figure. Accepted by The Journal of Geometric Analysis (2020)

References in corpus (2)

• Besov-ish spaces through atomic decomposition
• Transfer operators and atomic decomposition

Cited by in corpus (3)

• Besov-ish spaces through atomic decomposition
• Transfer operators and atomic decomposition
• Transfer operators, atomic decomposition and the Bestiary