Operator-free sparse domination

Abstract We obtain a sparse domination principle for an arbitrary family of functions $f(x,Q)$ , where $x\in {\mathbb R}^{n}$ and Q is cube in ${\mathbb . When applied to operators, this result recovers our recent works [37, 39]. On the other hand, can be also non-operator objects. In particular, we show applications generalised Poincaré–Sobolev inequalities, tent spaces general dyadic sums. Moreover, flexibility allows us treat operators that are not localisable sense [39], as will demonstrate application vector-valued square functions.