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First we introduce the Bailleul-Hoshinos result [4], which links the theory of regularity structures and the paracontrolled calculus. As an application of their result, we give another algebraic proof of the multicomponent commutator estimate [3], which is a generalized version of the Gubinelli-Imkeller-Perkowskis commutator estimate [11, Lemma 2.4].
We extend the results in [6] to Besov spaces $B_{p,q}^alpha$ with $p,qin[1,infty]$ and $0<alpha<1$.
We start in this work the study of the relation between the theory of regularity structures and paracontrolled calculus. We give a paracontrolled representation of the reconstruction operator and provide a natural parametrization of the space of admissible models.
We prove a general equivalence statement between the notions of models and modelled distributions over a regularity structure, and paracontrolled systems indexed by the regularity structure. This takes in particular the form of a parametrisation of t
We give a short essentially self-contained treatment of the fundamental analytic and algebraic features of regularity structures and its applications to the study of singular stochastic PDEs.
In this paper, we establish an optimal dual version of trace estimate involving angular regularity. Based on this estimate, we get the generalized Morawetz estimates and weighted Strichartz estimates for the solutions to a large class of evolution eq