Boundedness of averaging operators on geometrically doubling metric spaces

We prove that averaging operators are uniformly bounded on L p for all geometrically doubling metric measure spaces and all 1 ≤ p < ∞, with bounds independent of the measure. From this result, the L p convergence of averages as r → 0 immediately follows

Bibliographic Details
Author: Aldaz, Jesús M.
Format: article
Publication Date:2019
Country:España
Institution:Universidad Autónoma de Madrid
Repository:Biblos-e Archivo. Repositorio Institucional de la UAM
Language:English
OAI Identifier:oai:repositorio.uam.es:10486/690787
Online Access:http://hdl.handle.net/10486/690787
https://dx.doi.org/10.5186/aasfm.2019.4430
Access Level:Open access
Keyword:Averaging operators
Goemetrically doubling metric spaces
Matemáticas
Description
Summary:We prove that averaging operators are uniformly bounded on L p for all geometrically doubling metric measure spaces and all 1 ≤ p < ∞, with bounds independent of the measure. From this result, the L p convergence of averages as r → 0 immediately follows