ROUGH PATH METRICS ON A BESOV-NIKOLSKII-TYPE SCALE.

It is known, since the seminal work [T. Lyons, Differential equations driven by rough signals, Rev. Mat. Iberoamericana, 14 (1998)], that the solution map associated to a controlled differential equation is locally Lipschitz continuous in q-variation, resp., 1/q-Hölder-type metrics on the space of rough paths, for any regularity 1/q ∈ (0, 1]. We extend this to a new class of Besov-Nikolskii-type metrics, with arbitrary regularity 1/q ∈ (0, 1] and integrability p ∈ [q,8], where the case p ∈ {q,8} corresponds to the known cases. Interestingly, the result is obtained as a consequence of known q-variation rough path estimates. [ABSTRACT FROM AUTHOR]