PreprintCC BY 4.0arXiv
A Tb type theorem for suppressed kernels
Abstract
In this article, a non-homogeneous Tb type theorem for arbitrary dimensional Calderón-Zygmund singular integral operators is proved. This is an extension of an analogous non-homogeneous Tb theorem for the Cauchy transform, in the planar setting, due to Nazarov, Treil and Volberg. The novelties of the present work are the change of dimension and the fact that the operators to which the theorem applies are not necessarily antisymmetric. The techniques used in the proof include, among others, suppressed kernels, decompositions in L2(μ), where μ is a Radon measure in ℝd, and a probabilistic argument resulting from taking averages of the operators involved.
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BibTeX
@misc{fernandezvilaseca2026type,
title = {{A $Tb$ type theorem for suppressed kernels}},
author = {Marina Fernàndez-Vilaseca},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2606.26401},
eprint = {2606.26401},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.26401},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A Tb type theorem for suppressed kernels
AU - Marina Fernàndez-Vilaseca
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2606.26401
UR - https://arxiv.org/abs/2606.26401
AB - In this article, a non-homogeneous Tb type theorem for arbitrary dimensional Calderón-Zygmund singular integral operators is proved. This is an extension of an analogous non-homogeneous Tb theorem for the Cauchy transform, in the planar setting, due to Nazarov, Treil and Volberg. The novelties of the present work are the change of dimension and the fact that the operators to which the theorem applies are not necessarily antisymmetric. The techniques used in the proof include, among others, suppressed kernels, decompositions in L^2(μ), where μ is a Radon measure in ℝ^d, and a probabilistic argument resulting from taking averages of the operators involved.
ER -