Estimates for the full maximal function on graded Lie groups
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866913196140396544 |
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| author | Cardona, Duván |
| author_facet | Cardona, Duván |
| contents | On $\mathbb{R}^n,$ a classical result due to Bourgain establishes the restricted weak $(\frac{n}{n-1},1)$ inequality for the full maximal function $M_F^{dσ}$ associated to the spherical averages. In this work we present an extension to Bourgain's result on graded Lie groups for a family of full maximal operators. We formulate this extension using the group Fourier transform of the measures under consideration and the symbols of (positive Rockland operators which are) positive left-invariant hypoelliptic partial differential operators on graded Lie groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_07086 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Estimates for the full maximal function on graded Lie groups Cardona, Duván Analysis of PDEs Functional Analysis Representation Theory On $\mathbb{R}^n,$ a classical result due to Bourgain establishes the restricted weak $(\frac{n}{n-1},1)$ inequality for the full maximal function $M_F^{dσ}$ associated to the spherical averages. In this work we present an extension to Bourgain's result on graded Lie groups for a family of full maximal operators. We formulate this extension using the group Fourier transform of the measures under consideration and the symbols of (positive Rockland operators which are) positive left-invariant hypoelliptic partial differential operators on graded Lie groups. |
| title | Estimates for the full maximal function on graded Lie groups |
| topic | Analysis of PDEs Functional Analysis Representation Theory |
| url | https://arxiv.org/abs/2401.07086 |