Related papers: A problem for Hankel measures on Hardy space
This article presents a simple characterization for entangled vectors in a finite dimensional Hilbert space $H$. The characterization is in terms of the coefficients of an expansion of the vector relative to an orthonormal basis for $H$.…
Let $L$ be a linear operator on $L^2(\mathbb R^n)$ generating an analytic semigroup $\{e^{-tL}\}_{t\ge0}$ with kernels having pointwise upper bounds and $p(\cdot):\ \mathbb R^n\to(0,1]$ be a variable exponent function satisfying the…
We obtain a differential characterization for the anisotropic Hardy space $H_A^p$ by identifying it with a parabolic Hardy space associated with a general continuous group. This allows $H_A^p$ to be defined using a parabolic differential…
In this article, we consider the following fractional {Hardy-type} inequality: \begin{align} \label{Fractional Hardy_abst} \int_{\mathbb{R}^N} |w(x)||u(x)|^p \mathrm{d}x \leq C \int_{\mathbb{R}^N \times \mathbb{R}^N}…
Packing measures and Hewitt-Stromberg measures on products of metric spaces are investigated. New product inequalities for packing and lower packing dimensions are esatblished and used to solve a problem of Hu and Taylor regarding packing…
If $\mu $ is a positive Borel measure on the interval $[0, 1)$, the Hankel matrix $\mathcal H_\mu =(\mu_{n,k})_{n,k\ge 0}$ with entries $\mu_{n,k}=\int_{[0,1)}t^{n+k}\,d\mu(t)$ induces formally the operator $$\mathcal{H}_\mu…
We study a characterization of slice Carleson measures and of Carleson measures for the both the Hardy spaces $H^p(\mathbb B)$ and the Bergman spaces $\mathcal A^p(\mathbb B)$ of the quaternionic unit ball $\mathbb B$. In the case of…
We prove a technical estimate needed in our recent solution of the completeness question for the non-orthogonal Mexican hat wavelet system, in $L^p$ for $1<p<2$ and in the Hardy space $H^p$ for $2/3 < p \leq 1$.
We prove some sharp Hardy inequalities for domains with a spherical symmetry. In particular, we prove an inequality for domains of the unit $n$-dimensional sphere with a point singularity, and an inequality for functions defined on the…
Four new examples of explicitly diagonalizable Hankel matrices depending on a parameter $k\in(0,1)$ are presented. The Hankel matrices are regarded as matrix operators on the Hilbert space $\ell^{2}(\mathbb{N}_{0})$ and the solution of the…
We introduce noncommutative weak Orlicz spaces associated with a weight and study their properties. We also define noncommutative weak Orlicz-Hardy spaces and characterize their dual spaces.
The goal of this article was the S^1-equivariant transversality-problem and the compactification-problem for the moduli spaces of (perturbed) PU(2)-monopoles. A substantially improved version entitled "Moduli spaces of PU(2)-monopoles…
We study the space of Ricci-flat Kahler metrics on a given Calabi-Yau manifold, pose a number of questions about their possible degenerations, and survey some recent results on these questions.
We consider weighted $L^p$-Hardy inequalities involving the distance to the boundary of a domain in the $n$-dimensional Euclidean space with nonempty boundary. Using criticality theory, we give an alternative proof of the following result…
Cosmological N-body simulations have revealed many empirical relationships of dark matter halos, yet the physical origin of these halo properties still remains unclear. On the other hand, the attempts to establish the statistical mechanics…
The role of Liouville operators in the study of dynamical systems through the use of occupation measures have been an active area of research in control theory over the past decade. This manuscript investigates Liouville operators over the…
In this note, we obtain a full characterization of radial Carleson measures for the Hilbert-Hardy space on tube domains over symmetric cones. For large derivatives, we also obtain a full characterization of the measures for which the…
If $\,\mu \,$ is a finite positive Borel measure on the interval $\,[0,1)$, we let $\,\mathcal H_\mu \,$ be the Hankel matrix $\,(\mu _{n, k})_{n,k\ge 0}\,$ with entries $\,\mu _{n, k}=\mu _{n+k}$, where, for $\,n\,=\,0, 1, 2, \dots $,…
A new analytical characterization of balls in the Euclidean space $\RR^m$ is obtained. Unlike previous results of this kind, using either harmonic functions or solutions to the modified Helmholtz equation, the present one is based on…
We introduce a Banach rearrangement invariant (tail) quasy-norm by means of Hardy's (Cesaro) average on the (measurable) functions defined on some measurable space which is a slight generalization of classical Lorentz-Marcinkiewicz norm and…