Square function estimates for discrete Radon transforms

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Abstract

We show ℓp(ℤd )-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.

Original languageEnglish (US)
Pages (from-to)583-608
Number of pages26
JournalAnalysis and PDE
Volume11
Issue number3
DOIs
StatePublished - 2018
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics
  • Numerical Analysis

Keywords

  • Discrete harmonic analysis
  • Exponential sums
  • Hardy-Littlewood circle method
  • Radon operators

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