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arXiv · 2210.05786

Necessary cancellation conditions for the boundedness of operators on local Hardy spaces

Galia Dafni·Chun Ho Lau·Tiago Picon·Claudio Vasconcelos
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Abstract

In this work we present necessary cancellation conditions for the continuity of linear operators in $h^p(\mathbb{R}^n)$, $0<p\leq 1$, that map atoms into pseudo-molecules. Our necessary condition, expressed in terms of the $T^{\ast}$ condition, is the same as the one recently proved sufficient in [3], thus providing a necessary and sufficient cancellation condition for the boundedness of inhomogeneous Calder\'on--Zygmund type operators

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Galia Dafni, Chun Ho Lau, Tiago Picon, Claudio Vasconcelos. 2022-10-11. Necessary cancellation conditions for the boundedness of operators on local Hardy spaces. https://arxiv.org/abs/2210.05786

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