We show -boundedness, for , of discrete singular integrals of Radon type with the aid of appropriate square function estimates, which can be thought of as a discrete counterpart of Littlewood–Paley theory. It is a very robust approach which allows us to proceed as in the continuous case.
"Square function estimates for discrete Radon transforms." Anal. PDE 11 (3) 583 - 608, 2018. https://doi.org/10.2140/apde.2018.11.583