# Weighted L\'epingle inequality

## TL;DR

This paper establishes a new estimate for weighted p-th moments of martingale pathwise r-variation, relating it to the A_p characteristic of the weight, using a novel proof technique that avoids real interpolation.

## Contribution

It introduces a new proof method for weighted inequalities in martingale variation without relying on real interpolation techniques.

## Key findings

- Derived an estimate linking weighted p-th moments to A_p characteristic.
- Provided a proof avoiding traditional real interpolation methods.
- Enhanced understanding of weighted martingale inequalities.

## 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.