Related papers: Harmonic Besov spaces with small exponents

This paper is devoted to the study of the weighted Bergman space $A_\omega^p $ in the unit ball $\mathbb{B}$ of $\mathbb{C}^n$ with doubling weight $\omega$ satisfying $$\int_r^1\omega(t)dt <C \int_{\frac{1+r}{2}}^1\omega(t)dt ,\,\, 0\leq…

This paper aims to characterize boundedness of composition operators on Besov spaces $B^s_{p,q}$ of higher order derivatives $s>1+1/p$ on the one-dimensional Euclidean space. In contrast to the lower order case $0<s<1$, there were a few…

We prove that if a weight is a Bekoll\'{e}-Bonami weight for some $q$ and it satisfies another simple condition that depends on $0 < p < \infty$, then the operator taking a function to its harmonic conjugate is bounded on the harmonic…

Let $p\in(0,1)$, $\alpha:=1/p-1$ and, for any $\tau\in [0,\infty)$, $\Phi_{p}(\tau):=\tau/(1+\tau^{1-p})$. Let $H^p(\mathbb R^n)$, $h^p(\mathbb R^n)$ and $\Lambda_{n\alpha}(\mathbb{R}^n)$ be, respectively, the Hardy space, the local Hardy…

The aim of the paper is to establish (local) optimal embeddings of Besov spaces $B^{0,b}_{p,r}$ involving only a slowly varying smoothness $b$. In general, our target spaces are outside of the scale of Lorentz-Karamata spaces and are…

The paper deals with continuous and compact mappings generated by the Fourier transform between distinguished Besov spaces $B^s_p(\mathbb{R}^n) = B^s_{p,p}(\mathbb{R}^n)$, $1\le p \le \infty$, and between Sobolev spaces…

In this paper we study boundary value problems for higher order elliptic differential operators in divergence form. We establish well posedness for problems with boundary data in Besov spaces $\dot B^{p,p}_s$, $p\leq 1$, given well…

We establish wavelet characterizations of homogeneous Besov spaces on stratified Lie groups, both in terms of continuous and discrete wavelet systems. We first introduce a notion of homogeneous Besov space $\dot{B}_{p,q}^s$ in terms of a…

The canonical generalizations of two classical norms on Besov spaces are shown to be equivalent even in the case of non-linear Besov spaces, that is, function spaces consisting of functions taking values in a metric space and equipped with…

We use the method of atomic decomposition to build new families of function spaces, similar to Besov spaces, in measure spaces with grids, a very mild assumption. Besov spaces with low regularity are considered in measure spaces with good…

We study multiplication as well as Nemytskij operators in anisotropic vector-valued Besov spaces $B^{s, \omega}_p$, Bessel potential spaces $H^{s, \omega}_p$, and Sobolev-Slobodeckij spaces $W^{s, \omega}_p$. Concerning multiplication we…

Let $\Gamma$ be a bounded Jordan curve and $\Omega_i,\Omega_e$ its two complementary components. For $p\in (1, \infty),\,s\in(0,1)$ we define the two spaces $\mathcal{B}_{p,p}^s(\Omega_{i,e})$ as the set of harmonic functions $u$…

The inclusions between the Besov spaces $B^q$, the Bloch space $\mathcal{B}$ and the standard weighted Bergman spaces $A^p_\alpha$ are completely understood, but the norms of the corresponding inclusion operators are in general unknown. In…

In this paper we introduce Besov-type spaces with variable smoothness and integrability. We show that these spaces are characterized by the $\varphi $-transforms in appropriate sequence spaces and we obtain atomic decompositions for these…

In this article, we study harmonic symmetries on the compact locally conformally K\"{a}hler manifold $M$ of $dim_{\mathbb{C}}=n$. The space of harmonic symmetries is a subspace of harmonic differential forms which defined by the kernel of a…

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 paper we give a characterization of $\log J_f$ belongs to $\widetilde{\mathcal{B}}_p$ or $\widetilde{\mathcal{Q}}_p$ spaces for any locally univalent sense-preserving harmonic mappings $f$ defined in the unit disk, using the…

This paper develops a theory of Besov spaces $\dot{\mathbf{B}}^{\sigma}_{p,q} (N)$ and Triebel-Lizorkin spaces $\dot{\mathbf{F}}^{\sigma}_{p,q} (N)$ on an arbitrary homogeneous group $N$ for the full range of parameters $p, q \in (0,…

We study the embedding of integrable Teichm\"uller spaces $T_p$ into analytic Besov spaces via pre-Schwarzian derivatives. In contrast to the Bers embedding by Schwarzian derivatives, a significant difference arises between the cases $p>1$…

The aim of this paper is to study properties of Besov-type spaces with variable smoothness. We show that these spaces are characterized by the phi-transforms in appropriate sequence spaces and we obtain atomic decompositions for these…