ﻻ يوجد ملخص باللغة العربية
We construct explicit examples of Frostman-type measures concentrated on arbitrary planar rectifiable curves of positive length. Based on such constructions we obtain for each $p in (1,infty)$ an exact description of the trace space of the first-order Sobolev space $W^{1}_{p}(mathbb{R}^{2})$ to an arbitrary planar rectifiable curve $Gamma subset mathbb{R}^{2}$ of positive length.
Let $S subset mathbb{R}^{n}$ be a~closed set such that for some $d in [0,n]$ and $varepsilon > 0$ the~$d$-Hausdorff content $mathcal{H}^{d}_{infty}(S cap Q(x,r)) geq varepsilon r^{d}$ for all cubes~$Q(x,r)$ centered in~$x in S$ with side length $2r i
Let $S subset mathbb{R}^{n}$ be an arbitrary nonempty compact set such that the $d$-Hausdorff content $mathcal{H}^{d}_{infty}(S) > 0$ for some $d in (0,n]$. For each $p in (max{1,n-d},n]$ an almost sharp intrinsic description of the trace space $W_{p
A complete description of traces on $mathbb{R}^{n}$ of functions from the weighted Sobolev space $W^{l}_{1}(mathbb{R}^{n+1},gamma)$, $l in mathbb{N}$, with weight $gamma in A^{rm loc}_{1}(mathbb{R}^{n+1})$ is obtained. In the case $l=1$ the proof of
Wavelet set wavelets were the first examples of wavelets that may not have associated multiresolution analyses. Furthermore, they provided examples of complete orthonormal wavelet systems in $L^2(mathbb{R}^d)$ which only require a single generating w
We consider spaces of smooth immersed plane curves (modulo translations and/or rotations), equipped with reparameterization invariant weak Riemannian metrics involving second derivatives. This includes the full $H^2$-metric without zero order terms.