Journal
JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES
Volume 149, Issue -, Pages 216-253Publisher
ELSEVIER
DOI: 10.1016/j.matpur.2020.12.007
Keywords
Fractional Orlicz-Sobolev spaces; Sobolev embeddings; Hardy inequalities; Orlicz spaces; Rearrangement-invariant spaces
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Funding
- Italian Ministry of Education, University and Research (MIUR) [201758MTR2]
- Italian INdAM - National Institute of High Mathematics
- Czech Science Foundation [P201-18-00580S]
- Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany's Excellence Strategy [GZ 2047/1, 390685813]
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The paper presents the optimal Orlicz target space for embeddings of fractional-order Orlicz-Sobolev spaces in R-n, and establishes an improved embedding with an Orlicz-Lorentz target space that is optimal in the broader class of all rearrangement-invariant spaces. The study considers spaces of order s is an element of (0, 1), as well as higher-order spaces, and proposes related Hardy type inequalities.
The optimal Orlicz target space is exhibited for embeddings of fractional-order Orlicz-Sobolev spaces in R-n. An improved embedding with an Orlicz-Lorentz target space, which is optimal in the broader class of all rearrangement-invariant spaces, is also established. Both spaces of order s is an element of (0, 1), and higher-order spaces are considered. Related Hardy type inequalities are proposed as well. (C) 2020 Elsevier Masson SAS. All rights reserved.
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