Oscillation and jump inequalities for the polynomial ergodic averages along multi-dimensional subsets of primes

Abstract

We prove the uniform oscillation and jump inequalities for the polynomial ergodic averages modeled over multi-dimensional subset of primes. These inequalities provide endpoints for the $r$-variational estimates obtained by Trojan arXiv:1803.05406.

arXiv comment25 pages,no figures. This is the revised version, incorporating suggestions from the refere report. Accepted for publication in Mathematische Annalen

References in corpus (7)

• Variation estimates for averages along primes and polynomials
• A bootstrapping approach to jump inequalities and their applications
• Jump inequalities for translation-invariant operators of Radon type on ${\mathbb{Z}}^d$
• Jump inequalities via real interpolation
• Square function estimates for discrete Radon transforms
• (Uniform) Convergence of Twisted Ergodic Averages
• Oscillation estimates for truncated singular Radon operators