Related papers: Variable Besov-type spaces

We develop a comprehensive theory for a general class of multi-parameter function spaces of Besov-Triebel-Lizorkin type, with a matrix weight. We prove the equivalence of different quasi-norms, the identification of function and sequence…

We prove sharp radial estimates using Besov spaces. We also prove the propagation of singularities in Besov spaces.

Let $s\in{\mathbb R}$, $q\in (0,\infty]$, and $\tau\in[0,\infty)$. It is well known that Besov-type spaces $\dot B^{s,\tau}_{p,q}$ with $p\in (0,\infty]$ and Triebel--Lizorkin-type spaces $\dot F^{s,\tau}_{p,q}$ with $p\in (0,\infty)$ when…

We introduce and investigate classes of normed or quasinormed distribution spaces of generalized smoothness that can be obtained by various interpolation methods applied to classical Sobolev, Nikolskii-Besov, and Triebel-Lizorkin spaces. An…

In this paper we investigate Besov-Morrey spaces $\mathcal{N}^{s}_{u,p,q}(\Omega)$ and Besov-type spaces $B^{s,\tau}_{p,q}(\Omega)$ of positive smoothness defined on Lipschitz domains $\Omega \subset \mathbb{R}^d$ as well as on…

We provide a complete characterization of compactness of Sobolev embeddings of radially symmetric functions on the entire space $\mathbb{R}^n$ in the general framework of rearrangement-invariant function spaces. We avoid any unnecessary…

This article considers the Lipschitz space with mixed logarithmic smoothness of $2\pi$ periodic functions of several variables. We obtain equivalent descriptions of the norm of the Lipschitz space and prove embedding theorems between Besov…

We study harmonic Besov spaces $b^p_\alpha$ on the unit ball of $\mathbb{R}^n$, where $0<p<1$ and $\alpha\in\mathbb{R}$. We provide characterizations in terms of partial and radial derivatives and certain radial differential operators that…

In this article, via certain lower bound conditions on the measures under consideration, the authors fully characterize the Sobolev embeddings for the scales of Haj{\l}asz-Triebel-Lizorkin and Haj{\l}asz-Besov spaces in the general context…

In the present paper we study embedding operators for weighted Sobolev spaces whose weights satisfy the well-known Muckenhoupt A_p-condition. Sufficient conditions for boundedness and compactness of the embedding operators are obtained for…

We characterize the Besov spaces associated to the Gelfand pairs on the Heisenberg group. The characterization is given in terms of bandlimited wavelet coefficients where the bandlimitedness is introduced using spherical Fourier transform.…

In this note we revisit a result in [9], where we established nonlocal isoperimetric inequalities and the related embeddings for Besov spaces adapted to a class of H\"ormander operators of Kolmogorov-type. We provide here a new proof which…

This paper is concerned with the regularity of solutions to linear and nonlinear evolution equations extending our findings in [22] to domains of polyhedral type. In particular, we study the smoothness in the specific scale…

The paper is dedicated to the study of embeddings of the anisotropic Besov spaces $B^{\beta_1,...,beta_n}_{p;\theta_1,...,\theta_n}(\Bbb R^n)$ into Lorentz spaces. We find the sharp asymptotic behaviour of embedding constants when some of…

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…

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 problems in the context of the theoretical foundation of adaptive (wavelet) algorithms for the numerical treatment of operator equations. It is well-known that the analysis of such schemes naturally leads to…

In this paper we prove the Jawerth-Franke embeddings of Herz-type Besov and Triebel-Lizorkin spaces. Moreover, we obtain the Jawerth-Franke embeddings of Besov and Triebel-Lizorkin spaces equipped with power weights. An application we…

Motivated by a variety of representations of fractional powers of operators, we develop the theory of abstract Besov spaces $B^{ s, A }_{ q, X }$ for non-negative operators $A$ on Banach spaces $X$ with a full range of indices $s \in…

We define and study Sobolev spaces associated with Jacobi expansions. We prove that these Sobolev spaces are isomorphic to Jacobi potential spaces. As a technical tool, we also show some approximation properties of Poisson-Jacobi integrals.