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arXiv · 2401.13130

Sparse Domination of Singular Bilinear Forms on Non-Homogeneous spaces

Paco Villarroya
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Abstract

We introduce a new sparse $T1$ theorem that estimates the dual pair associated with a Calderon-Zygmund operator by a sub-bilinear form supported on a sparse family of cubes. The main result in the paper improves previous sparse $T1$ theorems in several ways: it applies to non-homogeneous measures of power growth, it only requires a numerable family of testing conditions, and it can be used to prove boundedness of Calderon-Zygmund operators on weighted spaces for a class of weights larger than the Muckenhoupt $A_p$ weights.

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Paco Villarroya. 2024-01-23. Sparse Domination of Singular Bilinear Forms on Non-Homogeneous spaces. https://arxiv.org/abs/2401.13130

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