Fefferman–Stein Inequalities for the Hardy–Littlewood Maximal Function on the Infinite Rooted k-ary Tree
In this paper, weighted endpoint estimates for the Hardy–Littlewood maximal function on the infinite rooted k-ary tree are provided. Motivated by Naor and Tao [ 23], the following Fefferman–Stein estimate w({x∈T:Mf(x)>λ})≤cs1λ∫T|f(x)|M(ws)(x)1sdxs>1 is settled, and moreover, it is shown that i...
| Authors: | , , |
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| Format: | article |
| Status: | Published version |
| Publication Date: | 2020 |
| Country: | Argentina |
| Institution: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repository: | CONICET Digital (CONICET) |
| Language: | English |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/129310 |
| Online Access: | http://hdl.handle.net/11336/129310 |
| Access Level: | Open access |
| Keyword: | WEIGHTS MAXIMAL FEFFERMAN-STEIN TREES https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Summary: | In this paper, weighted endpoint estimates for the Hardy–Littlewood maximal function on the infinite rooted k-ary tree are provided. Motivated by Naor and Tao [ 23], the following Fefferman–Stein estimate w({x∈T:Mf(x)>λ})≤cs1λ∫T|f(x)|M(ws)(x)1sdxs>1 is settled, and moreover, it is shown that it is sharp, in the sense that it does not hold in general if s=1. Some examples of nontrivial weights such that the weighted weak type (1,1) estimate holds are provided. A strong Fefferman–Stein-type estimate and as a consequence some vector-valued extensions are obtained. In the appendix, a weighted counterpart of the abstract theorem of Soria and Tradacete [ 38] on infinite trees is established. |
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