A truncated real interpolation method and characterizations of screened Sobolev spaces

Traces for homogeneous Sobolev spaces in infinite strip-like domains

In this paper we construct a trace operator for homogeneous Sobolev spaces defined on infinite strip-like domains. We identify an intrinsic seminorm on the resulting trace space that makes the trace operator bounded and allows us to construct a bounded right inverse. The intrinsic seminorm involves two features not encountered in the trace theory of bounded Lipschitz domains or half-spaces. First, due to the strip-like structure of the domain, the boundary splits into two infinite disconnected components. The traces onto each component are not completely independent, and the intrinsic seminorm…

Fractional Sobolev spaces with power weights

We investigate the form of the closure of the smooth, compactly supported functions $C_{c}^{\infty}(Ω)$ in the weighted fractional Sobolev space $W^{s,p;\,w,v}(Ω)$ for bounded $Ω$. We focus on the weights $w,\,v$ being powers of the distance to the boundary of the domain. Our results depend on the lower and upper Assouad codimension of the boundary of $Ω$. For such weights we also prove the comparability between the full weighted fractional Gagliardo seminorm and the truncated one.

有界域上截断分数阶微分方程的非局部边界条件

Nonlocal Boundary Conditions for Truncated-Fractional Differential Equations Posed on Bounded Domains

本文研究有界域上截断分数阶微分方程的非局部边界条件，证明仅要求函数在领圈上为零会导致分部积分、延拓及不等式等关键性质失效，需引入更小空间，并提出新提升算子、修正格林定理。

Approximation in Hankel Sobolev Space by Circular prolate spheroidal series

Recently, with the progress of science and the characteristic properties that distinguish the Slepian system called Prolate spheroidal wave functions from the others orthonormal systems, it became clear its important contributions in several areas such as mathematical statistics, signal processing, numerical analysis etc...The main issue of this work is to establish the convergence quality of the truncated error of a function $f$ from the Hankel Sobolev space $\mathcal{H}_α^r$, $r > 0$ and $α\geq -1/2$, by a generalized prolate spheroidal wave functions basis in $L^2$ norm. In the meantime, we…