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arXiv · 1512.07524

Square function estimates for discrete Radon transforms

Mariusz Mirek
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Abstract

We show $\ell^p\big(\mathbb Z^d\big)$ 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.

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Mariusz Mirek. 2015-12-23. Square function estimates for discrete Radon transforms. https://doi.org/10.2140/apde.2018.11.583

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