Related papers: Besov-Type Spaces with Variable Smoothness and Int…
We introduce truncated Besov and Triebel--Lizorkin function spaces and investigate their main properties: embeddings, interpolation, duality, lifting, traces. These new scales allow us to improve several known results in functional analysis…
We apply spectral theoretic methods to obtain a Littlewood-Paley decomposition of abstract inhomogeneous Besov spaces in terms of "smooth" and "bandlimited" functions. Well-known decompositions in several contexts are as special examples…
In this article, the authors introduce Besov and Triebel-Lizorkin spaces on spaces of homogeneous type in the sense of Coifman and Weiss, prove that these (in)homogeneous Besov and Triebel-Lizorkin spaces are independent of the choices of…
This paper investigates functional inequalities involving Besov spaces and functions of bounded variation, when the underlying metric measure space displays different local and global structures. Particular focus is put on the $L^1$ theory…
In this paper, different characterizations of the Besov-Dunkl spaces are given. We provide equivalence between these characterizations, using the Dunkl translation, the Dunkl transform and the Peetre K-functional.
We study embeddings of Besov-Morrey spaces ${\cal N}^{s}_{u,p,q}}({\mathbb R}^d)$ and of Triebel-Lizorkin-Morrey spaces ${\cal E}^{s}_{u,p,q}}({\mathbb R}^d)$ in the limiting cases when the smoothness $s$ equals $s_0=d\max(1/u-p/u,0)$ or…
This paper is concerned with proving some embeddings of the form \begin{equation*} F_{p_{1},q}^{s_{1}}\cdot B_{p_{2},\infty }^{s_{2}}\cdot ...\cdot B_{p_{m},\infty }^{s_{m}}\hookrightarrow F_{p,q}^{s_{1}},\quad m\geq 2. \end{equation*} The…
In this paper we obtain the non-asymptotic norm estimations of Besov's type between the norms of a functions in different Bilateral Grand Lebesgue spaces (BGLS). We also give some examples to show the sharpness of these inequalities.
There are two main aims of the paper. The first one is to extend the criterion for the precompactness of sets in Banach function spaces to the setting of quasi-Banach function spaces. The second one is to extend the criterion for the…
We develop the theory of variable exponent Hardy spaces. Analogous to the classical theory, we give equivalent definitions in terms of maximal operators. We also show that distributions in these spaces have an atomic decomposition including…
After proving the equivalence of the Bessel $K$-functional and the corresponding spherical modulus of smoothness we define fractional Bessel-Sobolev spaces. As an analog of the classical one the imbedding relation of fractional…
This paper has the characteristics of a review paper in which results of shift-invariant subspaces of Sobolev type are summarized without proofs. The structure of shift-invariant spaces $V_s$, $s\in\mathbb{R}$, generated by at most…
We develop properties of unramified, \'etale and smooth morphisms between Berkovich spaces over $\mathbb{Z}$. We prove that they satisfy properties analogous to those of morphisms of schemes and we provide analytification criteria. Our…
We use the author's previous work on atomic decompositions of Besov spaces with spectrum on symmetric cones, to derive new atomic decompositions for Bergman spaces on tube type domains. It is related to work by Ricci and Taibleson who…
We consider a range of geometric stability problems for hypersurfaces of spaceforms. One of the key results is an estimate relating the distance to a geodesic sphere of an embedded hypersurface with integral norms of the traceless Hessian…
For $0 < s < 1 < q < \infty$, we characterize the homeomorphisms $\varphi : \real^n \to \real^n$ for which the composition operator $f \mapsto f \circ \varphi$ is bounded on the homogeneous, scaling invariant Besov space…
In this article, we study the relation between Sobolev-type embeddings for Sobolev spaces or Besov spaces or Triebel-Lizorkin spaces defined either on a doubling or on a geodesic metric measure space and lower bound for measure of balls…
We characterize a weighted norm inequality which corresponds to the embedding of a class of absolutely continuous functions into the fractional order Sobolev space. The auxiliary result of the paper is of independent interest. It comprises…
Criteria for the fulfillment of inequalities in weighted smoothness function spaces of Besov type with Riemann-Liouville operators of natural orders on the real axis and semi-axes are found. The obtained estimates are refined under…
We study Sobolev spaces of radial functions on spherically symmetric Riemannian manifolds. Using geodesic polar coordinates, we give a sharp one-dimensional reduction: a radial function belongs to the Sobolev space on the manifold if and…