Martingale interpretation of weakly cancelling differential operators

TL;DR

This paper introduces martingale analogs of weakly cancelling differential operators and establishes a Sobolev-type embedding theorem within the martingale framework, bridging differential operator theory and martingale analysis.

Contribution

It presents a novel martingale interpretation of weakly cancelling differential operators and proves a corresponding Sobolev embedding theorem, expanding the theoretical understanding in this area.

Findings

Martingale analogs of weakly cancelling differential operators are developed.

A Sobolev-type embedding theorem is proved for these martingale operators.

The work bridges differential operator theory with martingale analysis.

Abstract

We provide martingale analogs of weakly cancelling differential operators and prove a Sobolev-type embedding theorem for these operators in the martingale setting.