Aalborg University

output

20022024

most citedDeep Learning for Audio Signal Processing

859 citations

Showing 2017 · math.APShow all

7 papers · 2 filters

math.AP2017★ 9 cited

Traces of Besov spaces revisited

Jon Johnsen

For the trace of Besov spaces $B_{p, q}^{s}$ onto a hyperplane, the borderline case with $s = \frac{n}{p} - (n - 1)$ and $0 < p < 1$ is analysed and a new dependence on the sum-exponent $q$ is…

math.AP2017

Regularity results and parametrices of semi-linear boundary problems of product type

Jon Johnsen

This short note describes the benefit one obtains from a specific construction of a family of parametrices for a class of elliptic boundary value problems perturbed by non-linear t…

math.AP2017★ 8 cited

Domains of type 1,1 operators: a case for Triebel--Lizorkin spaces

Jon Johnsen

Pseudo-differential operators of type 1,1 are proved continuous from the Triebel--Lizorkin space $F_{p, 1}^{d}$ to $L_{p}$ for $1 \leq p < \infty$ , when of order d, and this is the largest…

math.AP2017★ 12 cited

Domains of pseudo-differential operators: a case for the Triebel--Lizorkin spaces

Jon Johnsen

The main result is that every pseudo-differential operator of type 1,1 and order $d$ is continuous from the Triebel--Lizorkin space $F_{p, 1}^{d}$ to $L_{p}$ , $1 \leq p < \infty$ , and that…

math.AP2017★ 40 cited

A direct proof of Sobolev embeddings for quasi-homogeneous Lizorkin--Triebel spaces with mixed norms

Jon Johnsen, Winfried Sickel

The article deals with a simplified proof of the Sobolev embedding theorem for Lizorkin--Triebel spaces (that contain the $L_{p}$ -Sobolev spaces $H_{p}^{s}$ as special cases). The method…

math.AP2017★ 68 cited

On the trace problem for Triebel--Lizorkin spaces with mixed norms

Jon Johnsen, Winfried Sickel

The subject is traces of Sobolev spaces with mixed Lebesgue norms on Euclidean space. Specifically, restrictions to the hyperplanes given by the first and last coordinates are appl…