Related papers: Besov spaces induced by doubling weights
We continue our investigations on pointwise multipliers for Besov spaces of dominating mixed smoothness. This time we study the algebra property of the classes $S^r_{p,q}B(\mathbb{R}^d)$ with respect to pointwise multiplication. In addition…
We compute the norm of some bilinear forms on products of weighted Besov spaces in terms of the norm of their symbol in a space of pointwise multipliers defined in terms of Carleson measures.
In this paper, the authors first consider the bidirectional estimates of several typical integrals. As some applications of these integral estimates, the authors investigate the pointwise multipliers from the normal weight general function…
We study a class of nonlocal functionals in the spirit of the recent characterization of the Sobolev spaces $W^{1,p}$ derived by Bourgain, Brezis and Mironescu. We show that it provides a common roof to the description of the…
The purpose of this paper is to give a definition and prove the fundamental properties of Besov spaces generated by the Neumann Laplacian. As a by-product of these results, the fractional Leibniz rule in these Besov spaces is obtained.
We characterize the real interpolation space between a weighted $L^p$ space and a weighted Sobolev space in arbitrary bounded domains in $\mathbb{R}^n$, with weights that are positive powers of the distance to the boundary.
The tensorization problem for Sobolev spaces asks for a characterization of how the Sobolev space on a product metric measure space $X\times Y$ can be determined from its factors. We show that two natural descriptions of the Sobolev space…
We consider the dilation property of the modulation spaces $M^{p,q}$. Let $D_\lambda:f(t)\mapsto f(\lambda t)$ be the dilation operator, and we consider the behavior of the operator norm $\|D_\lambda\|_{M^{p,q}\to M^{p,q}}$ with respect to…
In this work we present a newly developed study of the interpolation of weighted Sobolev spaces by the complex method. We show that in some cases, one can obtain an analogue of the famous Stein-Weiss theorem for weighted $L^{p}$ spaces. We…
This monograph presents a comprehensive treatment of second order divergence form elliptic operators with bounded measurable t-independent coefficients in spaces of fractional smoothness, in Besov and weighted Sobolev classes. We establish…
We investigate the asymptotic behaviour of entropy and approximation numbers of the compact embedding $E^m_{p,\sigma}(B)\hookrightarrow L_p(B)$, $1\leq p<\infty,$ defined on the unit ball $B$ in $\mathbb{R}^n$. Here $E^m_{p,\sigma}(B)$…
A radially weighted Besov space $H$ is a space of holomorphic functions on the unit ball $\mathbb{B}_d \subseteq \mathbb{C}^d$ whose $N$-th radial derivative is square integrable with respect to a given admissible radial measure. We write…
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…
Let $B_{\alpha}^{p}$ be the space of $f$ holomorphic in the unit ball of $\Bbb C^n$ such that $(1-|z|^2)^\alpha f(z) \in L^p$, where $0<p\leq\infty$, $\alpha\geq -1/p$ (weighted Bergman space). In this paper we study the interpolating…
In this article, the authors introduce Besov-type spaces with variable smoothness and integrability. The authors then establish their characterizations, respectively, in terms of $\varphi$-transforms in the sense of Frazier and Jawerth,…
By classical results of Herglotz and F. Riesz, any bounded analytic function in the complex unit disk has a unique inner-outer factorization. Here, a bounded analytic function is called \emph{inner} or \emph{outer} if multiplication by this…
We introduce a new sphericalization mapping for metric spaces that is applicable in very general situations, including totally disconnected fractal type sets. For an unbounded complete metric space which is uniformly perfect at a base point…
In this paper, several refinements of the Berezin number inequalities are obtained. We generalize inequalities involving powers of the Berezin number for product of two operators acting on a reproducing kernel Hilbert space $\mathcal…
In the setting of $d$-variate periodic functions, often modelled as functions on the torus $\mathbb{T}^d\cong[0,1]^d$, the classical tensorized Fourier system is the system of choice for many applications. Turning to non-periodic functions…
We investigate the problem of establishing bilateral continuous embeddings of the uniformly localized Bessel potential spaces $H^{\gamma}_{r, \: unif}(\mathbb{R}^n)$ into the multiplier spaces between Bessel potential spaces with positive…