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arXiv · 2011.05637

A two weight local $Tb$ theorem for $n$-dimensional fractional singular integrals

Christos Grigoriadis·Michail Paparizos·Eric T. Sawyer·Chun-Yen Shen·Ignacio Uriarte-Tuero
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Abstract

We obtain a local two weight $Tb$ theorem with an energy side condition for higher dimensional fractional Calder\'{o}n-Zygmund operators. The proof follows the general outline of the proof for the corresponding one-dimensional $Tb$ theorem in [SaShUr12], but encountering a number of new challenges, including several arising from the failure in higher dimensions of T. Hyt\"{o}nen's one-dimensional two weight $A_{2}$ inequality [Hyt].

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Christos Grigoriadis, Michail Paparizos, Eric T. Sawyer, Chun-Yen Shen, Ignacio Uriarte-Tuero. 2020-11-11. A two weight local $Tb$ theorem for $n$-dimensional fractional singular integrals. https://arxiv.org/abs/2011.05637

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