Higher order div-curl type estimates for elliptic linear differential operators on localizable Hardy spaces

Catarina Machado; Tiago Picon

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arXiv · 2501.03307

Higher order div-curl type estimates for elliptic linear differential operators on localizable Hardy spaces

Catarina Machado·Tiago Picon

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Abstract

In this work, we establish higher-order div-curl type estimates in the sense of Coifman, Lions, Meyer & Semmes, in a local setting for elliptic homogeneous linear differential operators with smooth coefficients acting on localizable Hardy spaces. Our results imply and extend previously known estimates for first-order operators associated with elliptic systems and complexes of vector fields. As tools of independent interest, we develop a new smooth atomic decomposition for localizable Hardy-Sobolev spaces and prove a Poincar\'e-type inequality in this framework.

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Catarina Machado, Tiago Picon. 2025-01-06. Higher order div-curl type estimates for elliptic linear differential operators on localizable Hardy spaces. https://arxiv.org/abs/2501.03307

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