2025/03/26 by Kazaniecki, Krystian, Pawlewicz, Aleksander, Wojciechowski, Michał
#30H25 #46E35 #47B10 #FOS: Mathematics #Functional Analysis (math.FA)
paper · doi:10.48550/arxiv.2503.20478
The paper studies the factorization and summing properties of the Sobolev embedding operator. We propose two different approaches. One shows that the Sobolev embedding operator S:W1,1(\mathbbT2)\hookrightarrow L2(\mathbbT2) factorises through the identical embedding ℓΦ\hookrightarrowℓ2 for some Young function with Matuszewska-Orlicz index 1. Proof of this fact is based on two results of independent interest. First, a necessary and sufficient conditions on a Young function Φ and weight Ψ for boundedness of the embedding of the Sobolev space W1,1(\mathbbT2) into Besov-Orlicz space BΨΦ,1(\mathbbT2). Second, a generalization of the Marcinkiewicz sampling theorem to the context of Orlicz spaces. Another approach is based on the extrapolation of (p,1)-summing norm.