A rate of convergence of the solutions of the LANSα equations with periodic boundary to the solutions of the Navier-Stokes equations as α ↓ 0 is obtained in a mixed L1 − L2 time-space norm for small initial data in Besov-type function spaces in which global existence and uniqueness of solutions can also be established.

We prove the local well-posedness of the periodic stochastic Korteweg-de Vries equation with the additive space-time white noise. In order to treat low regularity of the white noise in space, we consider the Cauchy problem in the Besov-type space bbp,∞(T) for s = − 1 2 +, p = 2+ such that sp < −1. In establishing the local well-posedness, we use a variant of the Bourgain space with a weight fol...

Let G : R → R be a continuous function. Denote by TG the corresponding composition operator which sends f to G(f). Then we investigate consequences for the parameters s, p, and r of the inclusion TG (B p,q (R)) ⊂ B p,∞(R) . Here B p,q denotes a Besov space. 1991 Mathematics Subject Classification: 46E35, 47H30. Running title: Composition operators

In the present paper, we define for the Dunkl tranlation operators on the real line, the Besov–Dunkl space of functions for which the remainder in the generalized Taylor’s formula has a given order. We provide characterization of these spaces by the Dunkl convolution.

Bayesian solution of an inverse problem for indirect measurement M = AU + E is considered, where U is a function on a domain of R. Here A is a smoothing linear operator and E is Gaussian white noise. The data is a realization mk of the random variable Mk = PkAU + PkE, where Pk is a linear, finite dimensional operator related to measurement device. To allow computerized inversion, the unknown is...

We present forms of the classical Riesz–Kolmogorov theorem for compactness that are applicable in a wide variety settings. In particular, our theorems apply to classify precompact subsets Lebesgue space $$L^2$$ , Paley–Wiener spaces, weighted Bargmann–Fock and scale Besov–Sobolev spaces holomorphic functions includes Bergman general domains as well Hardy Dirichlet space. criteria characterize c...

We prove the local well-posedness of the three-dimensional Zakharov-Kuznetsov equation ∂tu+∆∂xu+u∂xu = 0 in the Sobolev spaces Hs(R3), s > 1, as well as in the Besov space B 2 (R 3). The proof is based on a sharp maximal function estimate in time-weighted spaces.

We study an initial value problem for the two-dimensional Euler equation. In particular, we consider the case where initial data belongs to a critical or subcritical Besov space, and initial vorticity is continuous with compact support. Under these assumptions, we conclude that the solution to the Euler equation loses an arbitrarily small amount of regularity as time evolves.

Exact order-of-magnitude estimates of the orthowidths and similar to them approximate characteristics Nikol’sky-Besov-type classes periodic single- multivariable functions in B1, 1 space have been obtained.

In this note we are concerned with interior regularity properties of the $p$-Poisson problem $\Delta_p(u)=f$ $p>2$. For all $0<\lambda\leq 1$ constuct right-hand sides $f$ differentiability $-1+\lambda$ such that (Besov-) smoothness corresponding solutions $u$ is essentially limited to $1+\lambda / (p-1)$. The statements local nature and cover integrability parameters. They particularly imply o...