#### Vol. 11, No. 3, 2018

 Recent Issues
 The Journal About the Journal Editorial Board Editors’ Interests Subscriptions Submission Guidelines Submission Form Policies for Authors Ethics Statement ISSN: 1948-206X (e-only) ISSN: 2157-5045 (print) Author Index To Appear Other MSP Journals
Square function estimates for discrete Radon transforms

### Mariusz Mirek

Vol. 11 (2018), No. 3, 583–608
##### Abstract

We show ${\ell }^{p}\left({ℤ}^{d}\right)$-boundedness, for $p\in \left(1,\infty \right)$, 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.

##### Keywords
discrete harmonic analysis, Radon operators, Hardy–Littlewood circle method, exponential sums
##### Mathematical Subject Classification 2010
Primary: 11L07, 42B20, 42B25