We revisit regularity of SLE trace, for all κ 6= 8, and establish Besov regularity under the usual half-space capacity parametrization. With an embedding theorem of Garsia–Rodemich–Rumsey type, we obtain finite moments (and hence almost surely) optimal variation regularity with index min(1 + κ/8, 2), improving on previous works of Werness, and also (optimal) Hölder regularity à la Johansson Vik...

This paper describes the many image decomposition models that allow to separate structures and textures or structures, textures, and noise. These models combined a total variation approach with di erent adapted functional spaces such as Besov or Contourlet spaces or a special oscillating function space based on the work of Yves Meyer. We propose a method to evaluate the performance of such algo...

We start by surveying a possible approach for function spaces of Besov type on special closed subsets of Rn. Afterwards we recall that, in the case of Sobolev spaces and Besov spaces on Rn, the Hausdorff dimension for the graphs of continuous functions belonging to such spaces has been studied by several authors, and that in the case of Besov spaces the final answer concerning the maximal possi...

Riesz potentials of fractal measures μ in metric spaces and their inverses are introduced . They define self–adjoint operators in the Hilbert space L2(μ) and the former are shown to be compact. In the Euclidean case the corresponding spectral asymptotics are derived with Besov space methods. The inverses of the Riesz potentials are fractal pseudodifferential operators. For the order two operato...

We establish new results on the space BV of functions with bounded variation. While it is well known that this space admits no unconditional basis, we show that it is “almost” characterized by wavelet expansions in the following sense: if a function f is in BV, its coefficient sequence in a BV normalized wavelet basis satisfies a class of weak-`1 type estimates. These weak estimates can be empl...

In a recent paper [12], Vishik proved the global wellposedness of the two-dimensional Euler equation in the critical Besov space B 2,1. In the present paper we prove that the Navier-Stokes system is globally well-posed in B 2,1, with uniform estimates on the viscosity. We prove also a global result of inviscid limit. The convergence rate in L is of order ν.

We pursue the study of the multiscale spaces Sν introduced by Jaffard in the context of multifractal analysis. We give the necessary and sufficient condition for Sν to be locally p-convex, and exhibit a sequence of p-norms that defines its natural topology. The strong topological dual of Sν is identified to another sequence space depending on ν, endowed with an inductive limit topology. As a pa...

We study the notion of molecules in coorbit spaces. The main result states that if an operator, originally defined on an appropriate space of test functions, maps atoms to molecules, then it can be extended to a bounded operator on coorbit spaces. For time-frequency molecules we recover some boundedness results on modulation spaces, for time-scale molecules we obtain the boundedness on homogeno...

In this paper, we consider the modified quasi-geostrophic equation ∂tθ + (u · ∇) θ + κΛθ = 0 u = Λα−1R⊥θ. with κ > 0, α ∈ (0, 1] and θ0 ∈ L2(R2). We remark that the extra Λα−1 is introduced in order to make the scaling invariance of this system similar to the scaling invariance of the critical quasi-geostrophic equations. In this paper, we use Besov space techniques to prove global existence an...