Sparse domination for the lattice Hardy-Littlewood maximal operator

17 Apr 2018 · Hänninen Timo S., Lorist Emiel ·

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.