Almost compact and compact embeddings of variable exponent spaces

0564919 - MÚ 2024 RIV PL eng J - Journal Article
Edmunds, D. E. - Gogatishvili, Amiran - Nekvinda, A.
Almost compact and compact embeddings of variable exponent spaces.
Studia mathematica. Roč. 268, č. 2 (2023), s. 187-211. ISSN 0039-3223. E-ISSN 1730-6337
R&D Projects: GA ČR(CZ) GA18-00580S
Institutional support: RVO:67985840
Keywords : almost-compact embeddings * Banach function spaces * variable Lebesgue spaces * variable Sobolev spaces
OECD category: Pure mathematics
Impact factor: 0.8, year: 2022
Method of publishing: Limited access

Let Ω be an open subset of R^N, and let p,q:Ω→(1,∞] be measurable functions. We give a necessary and sufficient condition for the embedding of the variable exponent space L^p(⋅)(Ω) in L^q(⋅)(Ω) to be almost compact. This leads to a condition on Ω ,p and q sufficient to ensure that the Sobolev space WL^{1,p(⋅)} (Ω) based on L^p(⋅)(Ω) is compactly embedded in L^q(⋅)(Ω), compact embedding results of this type already in the literature are included as special cases.
Permanent Link: https://hdl.handle.net/11104/0336493