A metric approach to sparse domination

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