Related papers: The Haar System in Besov-type Spaces

In this paper, we study different types of weighted Besov and Triebel-Lizorkin spaces with variable smoothness. The function spaces can be defined by means of the Littlewood-Paley theory in the field of Fourier analysis, while there are…

Let $1 \leq d < D$ and $(p,q,s)$ satisfying $0 < p < \infty$, $0 < q \leq \infty$, $0 < s-d/p < \infty$. In this article we study the global and local regularity properties of traces, on affine subsets of $\R^D$, of functions belonging to…

In this paper, we study the regularity of solutions to the $p$-Poisson equation for all $1<p<\infty$. In particular, we are interested in smoothness estimates in the adaptivity scale $ B^\sigma_{\tau}(L_{\tau}(\Omega))$, $1/\tau =…

We consider the classical Besov and Triebel-Lizorkin spaces defined via differences and prove a homogeneity property for functions with bounded support in the frame of these spaces. As the proof is based on compact embeddings between the…

Although numerous studies have focused on normal Besov spaces, limited studies have been conducted on exponentially weighted Besov spaces. Therefore, we define exponentially weighted Besov space $VB_{p,q}^{\delta,w}(\mathbb{R}^d)$ whose…

It is shown that under certain stability conditions a complemented subspace of the space $s$ of rapidly decreasing sequences is isomorphic to $s$ and this condition characterizes $s$. This result is used to show that for the classical…

In the setting of a doubling metric measure space, we study regularity of sets with finite $s$-perimeter, that is, sets whose characteristic functions have finite Besov energy, with regularity parameter $0<s<1$ and exponent $p=1$. Following…

By seeing whether a Liouville type theorem holds for positive, bounded, and/or finite energy $p$-harmonic and $p$-quasiharmonic functions, we classify proper metric spaces equipped with a locally doubling measure supporting a local…

Motivated by an open question going back to P.Malliavin and P.-A.Meyer (and closely related to the foundational work of S.Watanabe) on whether Malliavin-Watanabe-Sobolev regularity admits a characterization in terms of a holomorphic Laplace…

Let $X$ be a metric space and $\mu$ an $s$-regular Ahlfors measure. Let $Y$ be a metric space. We prove that for Besov functions $u \in B^r_{q,\infty}(X,\mu;Y)$, every point is a {\it general average Lebesgue point} of $u$ outside a…

An RD-space $\mathcal X$ is a space of homogeneous type in the sense of Coifman and Weiss with the additional property that a reverse doubling property holds in $\mathcal X$. In this paper, the authors first give several equivalent…

In this paper, a de Casteljau algorithm to compute (p,q)-Bernstein Bezier curves based on (p,q)-integers is introduced. We study the nature of degree elevation and degree reduction for (p,q)-Bezier Bernstein functions. The new curves have…

In this paper we develop a theory of Besov and Triebel--Lizorkin spaces on general noncompact Lie groups endowed with a sub-Riemannian structure. Such spaces are defined by means of hypoelliptic sub-Laplacians with drift, and endowed with a…

We describe the $(p,q)$ Fock--Carleson measures for weighted Fock--Sobolev spaces in terms of the objects $(s,t)$-Berezin transforms, averaging functions, and averaging sequences on the complex space $\mathbb{C}^n$. The main results show…

Let $\alpha\in\mathbb R$, $q\in(0,\infty]$, $p\in(0,\infty)$, and $W$ be an $A_p(\mathbb{R}^n,\mathbb{C}^m)$-matrix weight. In this article, the authors characterize the matrix-weighted Triebel-Lizorkin space $\dot{F}_{p}^{\alpha,q}(W)$ via…

We establish optimal continuity results for the action of the Hessian determinant on spaces of Besov type into the space of distributions on $\mathbb{R}^N$. In particular, inspired by recent work of Brezis and Nguyen on the distributional…

The article examines nonisotropic Nikolskii and Besov spaces with norms defined using $L_p$-averaged moduli of continuity of functions of appropriate orders along the coordinate directions, instead of moduli of continuity of known orders…

We study embeddings of Besov-type and Triebel-Lizorkin-type spaces, $id_\tau : {B}_{p_1,q_1}^{s_1,\tau_1}(\Omega) \hookrightarrow {B}_{p_2,q_2}^{s_2,\tau_2}(\Omega)$ and $id_\tau : {F}_{p_1,q_1}^{s_1,\tau_1}(\Omega) \hookrightarrow…

In this paper, we consider a new class of space, called $N(p, q, s)$-type spaces, in the unit ball $B$ of $C^n$. We study some basic properties, Hadamard gaps, Hadamard products, Random power series, Korenblum's inequality, Gleason's…

A typical approach to analysing statistical properties of expanding maps is to show spectral gaps of associated transfer operators in adapted function spaces. The classical function spaces for this purpose are H\"older spaces and Sobolev…