Calderón–Zygmund theory on some Lie groups of exponential growth
Abstract Let , where is a stratified Lie group and acts on via automorphic dilations. We prove that the group has the Calderón–Zygmund property, in the sense of Hebisch and Steger, with respect to a family of flow measures and metrics. This generalizes in various directions previous works by Hebisch and Steger and Martini et al., and provides a new approach in the development of the Calderón–Zygmund theory in Lie groups of exponential growth. We also prove a weak‐type (1,1) estimate for the Hardy–Littlewood maximal operator naturally arising in this setting.
Authors
- Filippo De Mari (ORCID: https://orcid.org/0000-0002-1097-690X)
- Matteo Levi (ORCID: https://orcid.org/0000-0002-6242-1770)
- Matteo Monti (ORCID: https://orcid.org/0000-0001-6848-5938)
- Maria Vallarino (ORCID: https://orcid.org/0000-0002-0023-9121)
Institutions
- Universitat Autònoma de Barcelona (ES)
- Politecnico di Torino (IT)
- Universitat de Barcelona (ES)
- University of Genoa (IT)
Publication Details
- Journal
- Mathematische Nachrichten
- Published
- 2024-11-04
- DOI
- https://doi.org/10.1002/mana.202300499
- Citations
- 1
- Primary Topic
- Advanced Harmonic Analysis Research
- Type
- article
- Field-Weighted Citation Impact
- 0.97
Funders
- Compagnia di San Paolo
- Generalitat de Catalunya
- Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni
- Spanish National Plan for Scientific and Technical Research and Innovation