Weighted and vector-valued variational estimates for ergodic averages

Abstract

We prove weighted and vector-valued variational estimates for ergodic averages on ${\mathbb{R}}^d$. The weighted square function estimate relating ergodic averages to the dyadic martingale is obtained using an ${\ell }^r$ version of a reverse Hölder inequality for variation seminorms.

v2: 12 pages, with a new short proof of the weighted bound for the square function

References in corpus (2)

• Weighted variation inequalities for differential operators and singular integrals in higher dimensions
• On Higher-Dimensional Oscillation in Ergodic Theory

Cited by in corpus (7)

• Weighted variation inequalities for differential operators and singular integrals in higher dimensions
• Sparse domination of sharp variational truncations
• Some jump and variational inequalities for the Calderón commutators and related operators
• Variational inequalities for the commutators of rough operators with BMO functions
• Quantitative weighted bounds for the $q$-variation of singular integrals with rough kernels
• Weighted jump and variational inequalities for rough operators
• Jump and variational inequalities for rough operators