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arXiv · 2009.00336

A metric approach to sparse domination

José M. Conde Alonso·Francesco Di Plinio·Ioannis Parissis·Manasa N. Vempati
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Abstract

We present a general approach to sparse domination based on single-scale $L^p$-improving as a key property. The results are formulated in the setting of metric spaces of homogeneous type and avoid completely the use of dyadic-probabilistic techniques as well as of Christ-Hytönen-Kairema cubes. Among the applications of our general principle, we recover sparse domination of Dini-continuous Calderón-Zygmund kernels on spaces of homogeneous type, we prove a family of sparse bounds for maximal functions associated to convolutions with measures exhibiting Fourier decay, and we deduce sparse estimates for Radon transforms along polynomial submanifolds of $\mathbb R^n$.

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José M. Conde Alonso, Francesco Di Plinio, Ioannis Parissis, Manasa N. Vempati. 2021-06-08. A metric approach to sparse domination. https://doi.org/10.1007/s10231-021-01174-7

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