Jump inequalities for translation-invariant operators of Radon type on ${\mathbb{Z}}^d$

Abstract

We prove strong jump inequalities for a large class of operators of Radon type in the discrete and ergodic theoretical settings. These inequalities are the $r=2$ endpoints of the $r$-variational estimates studied in arXiv:1512.07523.

v2: 39 pages, revised following referee report

References in corpus (2)

• A bootstrapping approach to jump inequalities and their applications
• Jump inequalities via real interpolation

Cited by in corpus (4)

• Oscillation estimates for truncated singular Radon operators
• Oscillation and jump inequalities for the polynomial ergodic averages along multi-dimensional subsets of primes
• Sparse bounds for discrete singular Radon transforms
• Bootstrap methods in bounding discrete Radon operators