English

Square function estimates for discrete Radon transforms

Classical Analysis and ODEs 2018-03-16 v1

Abstract

We show p(Zd)\ell^p\big(\mathbb Z^d\big) boundedness, for p(1,)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.

Keywords

Cite

@article{arxiv.1512.07524,
  title  = {Square function estimates for discrete Radon transforms},
  author = {Mariusz Mirek},
  journal= {arXiv preprint arXiv:1512.07524},
  year   = {2018}
}

Comments

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

R2 v1 2026-06-22T12:16:50.761Z