Dimension Independent Atomic Decomposition for Dyadic Martingale $$ \pmb {{\mathbb {H}}}^{1}$$

Abstract

AbstractWe introduce atoms for dyadic atomic $${\mathbb {H}}^1$$ H 1 for which the equivalence between the atomic and maximal function definitions is dimension independent. We give sharp, up to $$\log (d)$$ log ( d ) factor, estimates for the $${{\mathbb {H}}^1}\rightarrow L^1$$ H 1 → L 1 norm of the special maximal function.