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Local Hardy and bmo Spaces on Filtered Lie Groups
Abstract
We develop a theory of local Hardy and bmo spaces on a connected Lie group with polynomial growth whose Lie algebra is endowed with a filtration. Under suitable assumptions, we prove that the local Hardy spaces enjoy an appropriate atomic decomposition, are compatible with Calderón--Zygmund operators, and can be identified with certain Triebel--Lizorkin spaces, as it happens in the classical settings.
Related
- Besov and Triebel--Lizorkin Spaces on Filtered Lie Groups, III: the Spaces F∞,qα
- Besov and Triebel--Lizorkin Spaces on Filtered Lie Groups, II: Pointwise Multiplication, Localization, Differences
- Besov and Triebel--Lizorkin Spaces on Filtered Lie Groups with Polynomial Growth, I: Inclusions, Discretization, Duality
- Besov and Triebel-Lizorkin Spaces on Filtered Lie Groups with Polynomial Growth, II: Interpolation, Localization, Pointwise Multiplication
- The Local Embedding Problem for Hardy Spaces of Dirichlet Series
BibTeX
@misc{calzi2026local,
title = {{Local Hardy and bmo Spaces on Filtered Lie Groups}},
author = {Mattia Calzi and Elena Rizzo},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.38562},
eprint = {2610.38562},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.38562},
}
RIS
TY - UNPB
TI - Local Hardy and bmo Spaces on Filtered Lie Groups
AU - Mattia Calzi
AU - Elena Rizzo
PY - 2026
DA - 2026/10/28
PB - arXiv
DO - 10.48550/arxiv.2610.38562
UR - https://arxiv.org/abs/2610.38562
AB - We develop a theory of local Hardy and bmo spaces on a connected Lie group with polynomial growth whose Lie algebra is endowed with a filtration. Under suitable assumptions, we prove that the local Hardy spaces enjoy an appropriate atomic decomposition, are compatible with Calderón--Zygmund operators, and can be identified with certain Triebel--Lizorkin spaces, as it happens in the classical settings.
ER -