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Sharp conditions for the compactness of the Sobolev embedding on Musielak–Orlicz spaces
Author(s) -
Lang Jan,
Méndez Osvaldo
Publication year - 2019
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201700462
Subject(s) - mathematics , embedding , compact space , sobolev space , counterexample , pure mathematics , space (punctuation) , birnbaum–orlicz space , simple (philosophy) , interpolation space , mathematical analysis , discrete mathematics , functional analysis , computer science , artificial intelligence , biochemistry , chemistry , philosophy , epistemology , gene , operating system
We prove the compactness of the Sobolev embedding for Musielak–Orlicz spaces by way of simple conditions on the Matuszewska index of the underlying space. We provide counterexamples to show the sharpness of our conditions.