English

Notes on area operator, geometric 2-rough paths and Young integral when p^-1+q^-1=1

Classical Analysis and ODEs 2012-04-03 v1

Abstract

1.When equipped with 2-rough norm and restricted to continuous paths with bounded variation, the area operator is a closable unbounded operator. 2.The area defined through Riemann-Stieltjes integral is the only possible candidate to enhance a path with vanishing 2-variation into a geometric 2-rough path. 3.Young integral is extended to p^-1+q^-1=1 by assigning a finer scale continuity.

Keywords

Cite

@article{arxiv.1204.0112,
  title  = {Notes on area operator, geometric 2-rough paths and Young integral when p^-1+q^-1=1},
  author = {Danyu Yang},
  journal= {arXiv preprint arXiv:1204.0112},
  year   = {2012}
}
R2 v1 2026-06-21T20:42:50.916Z