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Jump inequalities for translation-invariant polynomial averages and singular integrals on $\mathbb Z^d$

Presenter
May 15, 2017
SLMath
Keywords:
  • harmonic analysis
  • singular integrals
  • discrete Radon transform
  • number theory
  • variational estimates
MSC:
  • 42-xx
  • 37A30
  • 37A45
  • 42B20
  • 43A77
Jump inequalities for translation-invariant polynomial averages and singular integrals on $\mathbb Z^d$ Thumbnail
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Abstract
The aim of this talk is to prove $\ell^p(\mathbb Z^d)$ inequalities with $1 < p < \infty$, for $\lambda$-jumps for discrete Radon transforms. These inequalities are the $r = 2$ endpoints of the $r$-variational estimates due to Mirek, Stein, and Trojan. This is a joint project with E.M. Stein and P. Zorin-Kranich.
Abstract