In this paper, we establish two embedding inequalities for the weighted Sobolev space and homogeneous endpoint Besov by using Hausdorff capacity. To do this, shall determine dual spaces of Choquet spaces.

We introduce a class of Möbius invariant spaces of analytic functions in the unit disk, characterize these spaces in terms of Carleson type measures, and obtain a necessary and sufficient condition for a lacunary series to be in such a space. Special cases of this class include the Bloch space, the diagonal Besov spaces, BMOA, and the so-called Qp spaces that have attracted much attention lately.

In this paper, we establish the global existence of small solutions to the inhomogeneous Navier-Stokes system in the half-space. The initial density only has to be bounded and close enough to a positive constant, and the initial velocity belongs to some critical Besov space. With a little bit more regularity for the initial velocity, those solutions are proved to be unique. In the last section ...

In this paper, we characterize holomorphic functions / such that the Hankel operators Hj are in the Schatten classes on bounded strongly pseudoconvex domains. It is proved that for p > In , Hj is in the Schatten class Sp if and only if / is in the Besov space Bp ; for p < In , Hj is in the Schatten class Sp if and only if / = constant.

We investigate compactness and asymptotic behaviour of the entropy numbers of embeddings B s1,s1 p1,q1 (R, U) ↪→ B s2,s2 p2,q2 (R, U) . Here B ′ p,q (Rn, U) denotes a 2-microlocal Besov space with a weight given by the distance to a fixed set U ⊂ Rn.

It is well known that, for 1 ≤ p < ∞, the diagonal Besov space Bp of the open unit ball admits a norm or semi-norm ‖ ‖p such that ‖f ◦ φ‖p = ‖f‖p for all f in Bp and all automorphisms φ of the unit ball. We show here that the same result holds when 0 < p < 1.

Riesz potentials and Laplacian of fractal measures in metric spaces are introduced. They deene self{adjoint operators in the Hilbert space L 2 () and the former are shown to be compact. In the euclidean case the corresponding spectral asymptotics are derived by Besov space methods. The inverses of the Riesz potentials are fractal pseudo-diierential operators. For the Laplace operator the spectr...

The Besov characteristic of a distribution f is the function sf defined for 0 ≤ t < ∞ by sf (t) = sup{ s ∈ R; f ∈ B 1/t,1(Rn) }. We give in this paper a criterion for a function Γ defined on [0,+∞[ to be the Besov characteristic of a distribution. Generalizations of this criterion to particular weighted Besov spaces and to anisotropic Besov spaces are also given.