Kernel estimates for the Weyl-Hörmander calculus, Weak (1,1) boundedness and other regularity properties
Abstract
We provide kernel estimates for pseudo-differential operators in the S(m,g) Weyl-Hörmander calculus classes. These new results lead to boundedness theorems like the weak (1,1) type for these classes and the boundedness of these operators from Hardy spaces to Lebesgue spaces Lp. We prove that under a suitable hypoelliticity condition on the weigh m, one can get the weak (1,1) inequality for the Fefferman order established previously by the second author in analogy to the classical Lp-boundedness theorem due to Fefferman. Our approach makes an extension to S(m,g) classes of previous estimates proved by Álvarez and Hounie, Nagase, Kumano-Go, etc, for the Hörmander classes including new regularity properties in this framework from the Hardy space Hp to Lp and also on Lorentz spaces. We have identified that the {\it Uniform Hörmander Condition} plays a fundamental role in some of our boundedness theorems.
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BibTeX
@misc{cardona2026kernel,
title = {{Kernel estimates for the Weyl-Hörmander calculus, Weak (1,1) boundedness and other regularity properties}},
author = {Duván Cardona and Julio Delgado and Manuel Martínez-Flores},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.21692},
eprint = {2609.21692},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.21692},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Kernel estimates for the Weyl-Hörmander calculus, Weak (1,1) boundedness and other regularity properties
AU - Duván Cardona
AU - Julio Delgado
AU - Manuel Martínez-Flores
PY - 2026
DA - 2026/09/18
PB - arXiv
DO - 10.48550/arxiv.2609.21692
UR - https://arxiv.org/abs/2609.21692
AB - We provide kernel estimates for pseudo-differential operators in the S(m,g) Weyl-Hörmander calculus classes. These new results lead to boundedness theorems like the weak (1,1) type for these classes and the boundedness of these operators from Hardy spaces to Lebesgue spaces L^p. We prove that under a suitable hypoelliticity condition on the weigh m, one can get the weak (1,1) inequality for the Fefferman order established previously by the second author in analogy to the classical L^p-boundedness theorem due to Fefferman. Our approach makes an extension to S(m,g) classes of previous estimates proved by Álvarez and Hounie, Nagase, Kumano-Go, etc, for the Hörmander classes including new regularity properties in this framework from the Hardy space H^p to L^p and also on Lorentz spaces. We have identified that the {\it Uniform Hörmander Condition} plays a fundamental role in some of our boundedness theorems.
ER -