Sparse domination for the lattice Hardy-Littlewood maximal operator

Abstract

We study the domination of the lattice Hardy--Littlewood maximal operator by sparse operators in the setting of general Banach lattices. We prove that the admissible exponents of the dominating sparse operator are determined by the $q$-convexity of the Banach lattice.

arXiv comment14 pages, improved presentation

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Cited by in corpus (9)

• Dyadic harmonic analysis and weighted inequalities: the sparse revolution
• Operator-free sparse domination
• Multi-scale sparse domination
• Euclidean structures and operator theory in Banach spaces
• Sparse domination implies vector-valued sparse domination
• Vector-valued extensions of operators through multilinear limited range extrapolation
• On pointwise ${\ell }^r$-sparse domination in a space of homogeneous type
• The ${\ell }^s$-boundedness of a family of integral operators on UMD Banach function spaces
• An Intersection Representation for a Class of Anisotropic Vector-valued Function Spaces