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
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| 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 |
| 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 |
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