Sparse Domination of Singular Bilinear Forms on Non-Homogeneous spaces

2024/01/23 by Paco Villarroya, Villarroya, Paco
Mathematics · #Advanced Harmonic Analysis Research #Geometry and complex manifolds #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2401.13130

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.

Related

• The Sparse T1 Theorem
• Sharp weighted estimates for multi-linear Calder 'on-Zygmund operators\n on non-homogeneous spaces
• Sparse domination via the Calderón-Zygmund decomposition: the example of Dini-smooth kernels
• New Local T1 Theorems on non-homogeneous spaces
• Uniform sparse domination of singular integrals via dyadic shifts