The main result is a Young-Stieltjes integral representation of the composition ϕ ∘ f of two functions f and ϕ such that for some α ∈ (0,1], ϕ has a derivative satisfying a Lipschitz condition of order α, and f has bounded p-variation for some p < 1 + α. If given α ∈ (0,1], the p-variation of f is bounded for some p < 2 + α, and ϕ has a second derivative satisfying a Lipschitz condition of order α, then a similar result holds with the Young-Stieltjes integral replaced by its extension.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm149-3-1,
author = {R. Norvai\v sa},
title = {Chain rules and p-variation},
journal = {Studia Mathematica},
volume = {151},
year = {2002},
pages = {197-238},
zbl = {1002.26006},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm149-3-1}
}
R. Norvaiša. Chain rules and p-variation. Studia Mathematica, Tome 151 (2002) pp. 197-238. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm149-3-1/