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arXiv · 1401.7841

Square Function Estimates in Spaces of Homogeneous Type and on Uniformly Rectifiable Euclidean Sets

Steve Hofmann·Dorina Mitrea·Marius Mitrea·Andrew J. Morris
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Abstract

We announce a local $T(b)$ theorem, an inductive scheme, and $L^p$ extrapolation results for $L^2$ square function estimates related to the analysis of integral operators that act on Ahlfors-David regular sets of arbitrary codimension in ambient quasi-metric spaces. The inductive scheme is a natural application of the local $T(b)$ theorem and it implies the stability of $L^2$ square function estimates under the so-called big pieces functor. In particular, this analysis implies $L^p$ and Hardy space square function estimates for integral operators on uniformly rectifiable subsets of the Euclidean space.

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Steve Hofmann, Dorina Mitrea, Marius Mitrea, Andrew J. Morris. 2014-01-30. Square Function Estimates in Spaces of Homogeneous Type and on Uniformly Rectifiable Euclidean Sets. https://arxiv.org/abs/1401.7841

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