4 papers
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…