A metric approach to sparse domination

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 ${\mathbb{R}}^n$.

arXiv comment36 pages, submitted for publication. V2: improvement of the main results Theorems A and B; uniform bound on the truncations is now required for some L^p unrelated to the sparse exponents; upgraded to Dini modulus of continuity; L^{p_j} improving assumption simplified. Applications are unchanged but verification is simplified

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Cited by in corpus (2)

• Operator-free sparse domination
• Multi-scale sparse domination