Related papers: Wavelet decomposition techniques and Hardy inequal…
The purpose of this article is twofold. The first is to strengthen fractional Sobolev type inequalities in Besov spaces via the classical Lorentz space. In doing so, we show that the Sobolev inequality in Besov spaces is equivalent to the…
In this article, the authors introduce the spaces of Lipschitz type on spaces of homogeneous type in the sense of Coifman and Weiss, and discuss their relations with Besov and Triebel-Lizorkin spaces. As an application, the authors…
In this paper novel classes of 2-D vector-valued spatial domain wavelets are defined, and their properties given. The wavelets are 2-D generalizations of 1-D analytic wavelets, developed from the Generalized Cauchy-Riemann equations and…
We study the Laplace operator on domains subject to Dirichlet or Neumann boundary conditions. We show that these operators admit a bounded $H^{\infty}$-functional calculus on weighted Sobolev spaces, where the weights are powers of the…
This paper constructs unique compactly supported functions in Sobolev spaces that have minimal norm, maximal support, and maximal central value, under certain renormalizations. They may serve as optimized basis functions in interpolation or…
This paper introduces a matrix analog of the Bessel processes, taking values in the closed set $E$ of real square matrices with nonnegative determinant. They are related to the well-known Wishart processes in a simple way: the latter are…
We consider function spaces of Besov, Triebel-Lizorkin, Bessel-potential and Sobolev type on $\R^d$, equipped with power weights $w(x) = |x|^\gamma$, $\gamma>-d$. We prove two-weight Sobolev embeddings for these spaces. Moreover, we…
In this paper we construct a wavelet basis in weighted L^2 of Euclidean space possessing vanishing moments of a fixed order for a general locally finite positive Borel measure. The approach is based on a clever construction of Alpert in the…
It is known that a smooth function of exponential decay at infinity can not be an orthonormal wavelet. Dziuba\'nski and Hern\'andez constructed smooth orthonormal wavelets of Gevrey type subexponential decay. We weaken the Gevrey type decay…
We study 2-microlocal Besov and Triebel-Lizorkin spaces with variable exponents on special Lipschitz domains. These spaces are as usual defined by restriction of the corresponding spaces on $\R^n$. In this paper we give two intrinsic…
Consider the discrete Laplacian $\Delta_d$ defined on the set of integers $\mathbb Z$ by \[ \Delta_d f(n) = -f(n+1) + 2f(n) -f(n-1), \ \ \ \ n\in \mathbb Z, \] where $f$ is a function defined on $\mathbb Z$. In this paper, we define Hardy…
A radial basis function (RBF) method based on matrix-valued kernels is presented and analyzed for computing two types of vector decompositions on bounded domains: one where the normal component of the divergence-free part of the field is…
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 propose a class of spherical wavelet bases for the analysis of geophysical models and forthe tomographic inversion of global seismic data. Its multiresolution character allows for modeling with an effective spatial resolution that varies…
In this paper, we develop the theory of Sobolev spaces on locally finite graphs, including completeness, reflexivity, separability, and Sobolev inequalities. Since there is no exact concept of dimension on graphs, classical methods that…
In this work, we consider "finite bandwidth" reproducing kernel Hilbert spaces which have orthonormal bases of the form $f_n(z)=z^n \prod_{j=1}^J \left( 1 - a_{n}w_j z \right)$, where $w_1 ,w_2, \ldots w_J $ are distinct points on the…
We establish trace theorems for function spaces defined on general Ahlfors regular metric spaces $Z$. The results cover the Triebel-Lizorkin spaces and the Besov spaces for smoothness indices $s<1,$ as well as the first order…
Sobolev embeddings, of arbitrary order, are considered into function spaces on domains of $\mathbb R^n$ endowed with measures whose decay on balls is dominated by a power $d$ of their radius. Norms in arbitrary rearrangement-invariant…
We derive basic properties of Triebel-Lizorkin-Lorentz spaces important in the treatment of PDE. For instance, we prove Triebel-Lizorkin-Lorentz spaces to be of class $\mathcal{HT}$, to have property $(\alpha)$, and to admit a multiplier…
In this paper we study weighted Hardy-Sobolev spaces of vector valued functions analytic on double-napped cones of the complex plane. We introduce these spaces as a tool for complex scaling of linear ordinary differential equations with…