BESOV SPACES ON DOMAINS IN Rd

A new class of function spaces on domains of R^d and its relations to classical function spaces

New Properties of Besov and Triebel-Lizorkin Spaces on RD-Spaces

An RD-space X is a space of homogeneous type in the sense of Coifman and Weiss with the additional property that a reverse doubling property holds in X . In this paper, the authors first give several equivalent characterizations of RD-spaces and show that the definitions of spaces of test functions on X are independent of the choice of the regularity ǫ ∈ (0, 1); as a result of this, the Besov a...

Spatial Besov regularity for semilinear stochastic partial differential equations on bounded Lipschitz domains

We study the spatial regularity of semilinear parabolic stochastic partial differential equations on bounded Lipschitz domains O ⊆ Rd in the scale Bα τ,τ (O), 1/τ = α/d + 1/p, p ≥ 2 fixed. The Besov smoothness in this scale determines the order of convergence that can be achieved by adaptive numerical algorithms and other nonlinear approximation schemes. The proofs are performed by establishing...

Persistence of the incompressible Euler equations in a Besov space B d + , ( R d )

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...

Decomposition of Weighted Triebel-lizorkin and Besov Spaces on the Ball

Weighted Triebel-Lizorkin and Besov spaces on the unit ball Bd in Rd with weights wμ(x) = (1 − |x|2)μ−1/2, μ ≥ 0, are introduced and explored. A decomposition scheme is developed in terms of almost exponentially localized polynomial elements (needlets) {φξ}, {ψξ} and it is shown that the membership of a distribution to the weighted Triebel-Lizorkin or Besov spaces can be determined by the size ...