Weighted Lépingle inequality

Abstract

We prove an estimate for weighted $p$-th moments of the pathwise $r$-variation of a martingale in terms of the $A_p$ characteristic of the weight. The novelty of the proof is that we avoid real interpolation techniques.

arXiv commentv2: 6 pages, added statement of the vector-valued Lépingle inequality in Remark 3.5

References in corpus (6)

• An elementary proof of the $A_2$ Bound
• Variation estimates for averages along primes and polynomials
• Canonical RDEs and general semimartingales as rough paths
• Sharp Reverse Hölder property for A_\infty weights on spaces of homogeneous type
• Jump inequalities via real interpolation
• Variational estimates for martingale paraproducts

Cited by in corpus (1)

• Rough semimartingales and $p$-variation estimates for martingale transforms