Analysis & PDE

  • Anal. PDE
  • Volume 11, Number 3 (2018), 583-608.

Square function estimates for discrete Radon transforms

Mariusz Mirek

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We show p(d)-boundedness, for p(1,), 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.

Article information

Anal. PDE, Volume 11, Number 3 (2018), 583-608.

Received: 18 June 2016
Revised: 22 July 2017
Accepted: 20 September 2017
First available in Project Euclid: 20 December 2017

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11L07: Estimates on exponential sums 42B20: Singular and oscillatory integrals (Calderón-Zygmund, etc.) 42B25: Maximal functions, Littlewood-Paley theory

discrete harmonic analysis Radon operators Hardy–Littlewood circle method exponential sums


Mirek, Mariusz. Square function estimates for discrete Radon transforms. Anal. PDE 11 (2018), no. 3, 583--608. doi:10.2140/apde.2018.11.583.

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