Year: 2024
Type: article
Abstract: This paper aims to study $$A_p$$ A p weights in the context of a class of metric measure spaces with exponential volume growth, namely infinite trees with root at infinity equipped with the geodesic distance and flow measures. Our main result is a Muckenhoupt Theorem, which is a characterization of the weights for which a suitable Hardy–Littlewood maximal operator is bounded on the corresponding weighted $$L^p$$ L p spaces. We emphasise that this result does not require any geometric assumption on the tree or any condition on the flow measure. We also prove a reverse Hölder inequality in the case when the flow measure is locally doubling. We finally show that the logarithm of an $$A_p$$ A p weight is in BMO and discuss the connection between $$A_p$$ A p weights and quasisymmetric mappings.
Source: Revista Matemática Complutense
Institutions: UNSW Sydney, Politecnico di Torino
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,990
Award: G5311024737
OpenAlex ID: W4402584316