The purpose of the present paper is to consider some weak asymptotic problems concerning the infinite-dimensional Kolmogorov widths, the infinite-dimensional linear widths, the infinite-dimensional Gel’fand widths and optimal recovery in Besov space. It is obvious to be found that the results obtained and methods used in Besov space are easily generalized, and hence in this paper these results ...

We establish optimal continuity results for the action of the Hessian determinant on spaces of Besov type into the space of distributions on RN . In particular, inspired by recent work of Brezis and Nguyen on the distributional Jacobian determinant, we show that the action is continuous on the Besov space of fractional order B(2 − 2 N , N) and, furthermore, that all continuity results in this s...

We are interested in the regularity of centered Gaussian processes (Z x (ω)) x∈M indexed by compact metric spaces (M, ρ). It is shown that the almost everywhere Besov space regularity of such a process is (almost) equivalent to the Besov regularity of the covariance K(x, y) = E(Z x Z y) under the assumption that (i) there is an underlying Dirichlet structure on M which determines the Besov spac...

This paper is dedicated to the proof of new maximal regularity results involving Besov spaces for the heat equation in the half-space or in bounded or exterior domains of R.We strive for time independent a priori estimates in regularity spaces of type L1(0,T ;X) where X stands for some homogeneous Besov space. In the case of bounded domains, the results that we get are similar to those of the w...

In this paper we use multiscale characteristics of wavelet decompositions and their relationship to smoothness spaces such as Besov spaces to derive a framework for smoothing and sharpening of signals and images. As a result, we derive a multiscale generalization of traditional techniques, such as unsharp masking, while using the smoothness parameter α in the Besov space Bα q (L p) to provide a...

Besov spaces classify signals and images through the Besov norm, which is based on a deterministic smoothness measurement. Recently, we revealed the relationship between the Besov norm and the likelihood of an independent generalized Gaussian wavelet probabilistic model. In this paper, we extend this result by providing an information-theoretic interpretation of the Besov norm as the Shannon co...

are considered. Here u(x, t) = (u,u, . . . ,ud) is the Eulerian velocity of a fluid flow and (u,∇)uk =∑di= u∂iu , k = , , . . . ,d with ∂i ≡ ∂ ∂xi . The best local existence and uniqueness results known for the Euler equations () in Besov spaces are a series of theorems on the space B p, (Rd) with  < p ≤ ∞ (see the introductions in [, ] for details and the references therein). The loc...

Mourre's commutator method is used together with Besov spaces, in this paper, to settle the question of uniqueness of solutions to the scattering problem for the acoustic wave propagation in perturbed stratiied uids in R n with n 2: The uniqueness of solutions is established by introducing a radiation condition in the framework of Besov spaces, and is then used to prove resolvent estimates in t...