Square function estimates for discrete Radon transforms

Abstract

We show ${\ell }^p\left({\mathbb{Z}}^d\right)$ boundedness, for $p\in (1,\infty )$, of discrete singular integrals of Radon type with the aid of appropriate square function estimates, which can be thought as a discrete counterpart of the Littlewood--Paley theory. It is a very powerful approach which allows us to proceed as in the continuous case.

19 pages, no figures. arXiv admin note: text overlap with arXiv:1512.07518

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