We address the question of which function spaces are invariant under the action of scalar conservation laws in one and several space dimensions. We establish two types of results. The rst result shows that if the initial data is in a rearrangement-invariant function space, then the solution is in the same space for all time. Secondly, we examine which smoothness spaces among the Besov spaces ar...

We discover a new relationship between two seemingly diierent image modeling methodologies; the Besov space theory and the wavelet-domain statistical image models. Besov spaces characterize the set of real-world images through a deterministic characterization of the image smoothness, while statistical image models capture the probabilistic properties of images. By establishing a relationship be...

We introduce and study the family of Besov–Köthe spaces which is a generalization of the Besov spaces, the Besov–Morrey spaces and the variable Besov spaces. As an application of the general results for the Besov–Köthe spaces, we identify a pre-dual of the Besov–Morrey space.

This paper concerns itself with Besov space solutions of the 2-D quasi-geostrophic (QG) equation with dissipation induced by a fractional Laplacian (−1)α . The goal is threefold: first, to extend a previous result on solutions in the inhomogeneous Besov space Br 2,q [J. Wu, Global solutions of the 2D dissipative quasi-geostrophic equation in Besov spaces, SIAM J. Math. Anal. 36 (2004–2005) 1014...

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...

We investigate Besov spaces and their connection with dyadic spline approximation in Lp(Cl), 0 < p < oo. Our main results are: the determination of the interpolation spaces between a pair of Besov spaces; an atomic decomposition for functions in a Besov space; the characterization of the class of functions which have certain prescribed degree of approximation by dyadic splines.

We define and characterize the harmonic Besov space Bp, 1 ≤ p ≤ ∞, on the unit ball B in Rn. We prove that the Besov spaces Bp, 1 ≤ p ≤ ∞, are natural quotient spaces of certain Lp spaces. The dual of Bp, 1 ≤ p < ∞, can be identified with Bq , 1/p + 1/q = 1, and the dual of the little harmonic Bloch space B0 is B1.

In this paper, we show the inclusion and the density of the Schwartz space in Besov–Dunkl spaces and we prove an interpolation formula for these spaces by the real method. We give another characterization for these spaces by convolution. Finally, we establish further results concerning integrability of the Dunkl transform of function in a suitable Besov–Dunkl space.

Two embeddings of a homogeneous endpoint Besov space are established via the Hausdorff capacity and the heat equation. Meanwhile, a co-capacity formula and a trace inequality are derived from the Besov space. © 2006 Elsevier Inc. All rights reserved. MSC: primary 31, 42A, 46E, 47B, 53A

Classical and nonclassical Besov and Triebel-Lizorkin spaces with complete range of indices are developed in the general setting of Dirichlet space with a doubling measure and local scale-invariant Poincaré inequality. This leads to Heat kernel with small time Gaussian bounds and Hölder continuity, which play a central role in this article. Frames with band limited elements of sub-exponential s...