Related papers: Kernels of trace operators via fine continuity

We investigate the tracial and ideal structures of $C^*$-algebras of quasi-regular representations of stabilizers of boundary actions. Our main tool is the notion of boundary maps, namely $\Gamma$-equivariant unital completely positive maps…

In the case of any bounded open set $\Omega$ $\subset$ R d with boundary $\partial$$\Omega$, we first construct a directional trace in any direction $\theta$ of the unit sphere, for any u $\in$ L 2 ($\Omega$) whose the directional…

We study fractal sets $\Gamma\subset \mathbb{R}^n$ with non-empty interior $\Omega$, that are attractors of iterated function systems (IFSs) of contracting similarities satisfying the open set condition. Examples for $n=2$ are the closures…

In this paper we study mapping properties of Toeplitz-like operators on weighted Bergman spaces of bounded strongly pseudconvex domains in $\mathbb{C}^n$. In particular we prove that a Toeplitz operator built using as kernel a weighted…

Let $M$ be an oriented even-dimensional Riemannian manifold on which a discrete group $\Gamma$ of orientation-preserving isometries acts freely, so that the quotient $X=M/\Gamma$ is compact. We prove a vanishing theorem for a half-kernel of…

We consider weakly positive semidefinite kernels valued in ordered $*$-spaces with or without certain topological properties, and investigate their linearisations (Kolmogorov decompositions) as well as their reproducing kernel spaces. The…

Let $(\operatorname{X},\operatorname{d},\mu)$ be a metric measure space with uniformly locally doubling measure $\mu$. Given $p \in (1,\infty)$, assume that $(\operatorname{X},\operatorname{d},\mu)$ supports a weak local $(1,p)$-Poincar\'e…

Let $M_{\Omega,\alpha}$ and $T_{\Omega,\alpha}$ be the fractional maximal and integral operators with rough kernels, where $0<\alpha<n$. In this paper, we shall study the continuity properties of $M_{\Omega,\alpha}$ and $T_{\Omega,\alpha}$…

Let E_lambda be a Hilbert space, whose elements are functions spanned by the eigenfunctions of the Laplace-Beltrami operator associated with an eigenvalue lambda>0. The norm of elements in this space is given by the Petersson inner product.…

A commuting tuple of operators $(S_1,\dots, S_{n-1},P)$, defined on a Hilbert space $\mathcal H$, for which the closed symmetrized polydisc \[ \Gamma_n =\left\{ \left(\sum_{1\leq i\leq n} z_i,\sum_{1\leq i<j\leq n}z_iz_j,\dots,…

Let $\Gamma$ be a finitely generated group acting by probability measure preserving maps on the standard Borel space $(X,\mu)$. We show that if $H\leq\Gamma$ is a subgroup with relative spectral radius greater than the global spectral…

The $L^p$-spaces, with $p \not = \infty$, form a partial algebra $(L^p(\Omega), \Gamma, \cdot)$ with pointwise multiplication of functions. The Sobolev spaces $W^{k,p}(\Omega)$, delineated by weak derivatives as subspaces of $L^p$-spaces is…

We prove a general criterion for the density in energy of suitable subalgebras of Lipschitz functions in the metric-Sobolev space $H^{1,p}(X,\mathsf{d},\mathfrak{m})$ associated with a positive and finite Borel measure $\mathfrak{m}$ in a…

We extend a localization result for the $H^{1/2}$ norm by B. Faermann to a wider class of subspaces of $H^{1/2}(\Gamma)$, and we prove an analogous result for the $H^{-1/2}(\Gamma)$ norm, $\Gamma$ being the boundary of a bounded polytopal…

We study properties of the semigroup $(e^{-tH})_{t\ge 0}$ on the space $L^ 2(\Gamma_X,\pi)$, where $\Gamma_X$ is the configuration space over a locally compact second countable Hausdorff topological space $X$, $\pi$ is a Poisson measure on…

Error estimates for kernel interpolation in Reproducing Kernel Hilbert Spaces (RKHS) usually assume quite restrictive properties on the shape of the domain, especially in the case of infinitely smooth kernels like the popular Gaussian…

The paper presents some weak compactness criterion for a subset $M$ of the set $\mathfrak{RM}_b(T,\mathcal{G})$ of all positive bounded Radon measures on a Hausdorff topological space $(T,\mathcal{G})$ similar to the Prokhorov criterion for…

We construct fractional Sobolev spaces on arbitrary time scales, both in one dimension and on product time scales. In 1D, we define $W^{\alpha(\cdot),p}_{\mathrm{rd}}(\mathcal I)$ through a variable-order Gagliardo-type seminorm and prove…

For a smoothly bounded strictly pseudoconvex domain, we describe the boundary singularity of weighted Bergman kernels with respect to weights behaving like a power (possibly fractional) of a defining function, and, more generally, of the…

We establish a pointwise limit theorem for a broad class of pa\-ra\-me\-ter-\-de\-pen\-dent BMO-type seminorms as the parameter tends to zero. By introducing novel BMO-type seminorms, we provide a unified framework that extends several…