We present a general approach to sparse domination based on single-scale Lp-improving as a key assumption. 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 Rn.
A metric approach to sparse domination / Conde-Alonso, J. M.; Di Plinio, F.; Parissis, I.; Vempati, M. N.. - In: ANNALI DI MATEMATICA PURA ED APPLICATA. - ISSN 0373-3114. - (2021). [10.1007/s10231-021-01174-7]
A metric approach to sparse domination
Di Plinio F.
;
2021
Abstract
We present a general approach to sparse domination based on single-scale Lp-improving as a key assumption. 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 Rn.File | Dimensione | Formato | |
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