Limiting conditions of Muckenhoupt and reverse H\'older classes on metric measure spaces

Autor:	Kurki, Emma-Karoliina
Rok vydání:	2022
Předmět:	Mathematics - Classical Analysis and ODEs 42B35 42B25 30L99
Druh dokumentu:	Working Paper
Popis:	The natural maximal and minimal functions commute pointwise with the logarithm on $A_\infty$. We use this observation to characterize the spaces $A_1$ and $RH_\infty$ on metric measure spaces with a doubling measure. As the limiting cases of Muckenhoupt $A_p$ and reverse H\"older classes, respectively, their behavior is remarkably symmetric. On general metric measure spaces, an additional geometric assumption is needed in order to pass between $A_p$ and reverse H\"older descriptions. Finally, we apply the characterization to give simple proofs of several known properties of $A_1$ and $RH_\infty$, including a refined Jones factorization theorem. In addition, we show a boundedness result for the natural maximal function. Comment: 14 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2204.01441 Zobrazit plný text záznamu View this record from Arxiv