6 papers · 1 filter
Non-strict singularity of optimal Sobolev embeddings
Jan Lang, ZdenÄk Mihula
We investigate the operator-theoretic property of strict singularity for optimal Sobolev embeddings within the general framework of rearrangement-invariant function spaces (r.i. sp…
Bases of Lebesgue spaces formed by neural networks
Vladimir Kulbatov, Jan Lang, Cornelia Schneider +1
The seminal work of Daubechies, DeVore, Foucart, Hanin, and Petrova introduced in 2022 a sequence of univariate piece-wise linear functions, which resemble the classical Fourier ba…
A Classification Theorem on Non-compact Embeddings between Besov Spaces
Chian Yeong Chuah, Jan Lang, Liding Yao
We analyze the embedding properties between Besov spaces, defined on the total space and on bounded domains. We give a complete classification on whether or not these…
A Bourgain-Gromov problem on non-compact Sobolev-Lorentz embeddings
Chian Yeong Chuah, Jan Lang, Liding Yao
We study the non-compact Sobolev embeddings into the optimal scale of Lorentz spaces, , where , $1 \le m…
Quality of non-compactness for Sobolev Embedding with one point non-compactness
Chian Yeong Chuah, Jan Lang
This paper investigates instances of Sobolev embeddings characterized by local compactness at every point within their domain, except for a single point. We obtain the sharp condit…
Maximal noncompactness of limiting Sobolev embeddings
Jan Lang, ZdenÄk Mihula, LuboÅ¡ Pick
We develop a new method suitable for establishing lower bounds on the ball measure of noncompactness of operators acting between considerably general quasinormed function spaces. T…