Where Sobolev interacts with Gagliardo–Nirenberg

Where Sobolev interacts with Gagliardo–Nirenberg

We investigate the validity of the fractional Gagliardo-Nirenberg-Sobolev inequality(1)‖f‖Wr,q(Ω)≲‖f‖Ws1,p1(Ω)θ‖f‖Ws2,p2(Ω)1−θ,∀f∈Ws1,p1(Ω)∩Ws2,p2(Ω). Here, s1,s2,r are non-negative numbers (not necessarily integers), 1≤p1,p2,q≤∞, and we assume, for some θ∈(0,1), the standard relations(2)r...

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Veröffentlicht in:Journal of functional analysis 2019-10, Vol.277 (8), p.2839-2864
Hauptverfasser: Brezis, Haïm, Mironescu, Petru
Format: Artikel
Sprache:eng
Schlagworte:
(Fractional) Sobolev spaces
Classical Analysis and ODEs
Gagliardo-Nirenberg-Sobolev inequalities
Interpolation inequalities
Mathematics
Sobolev embeddings
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Zusammenfassung:We investigate the validity of the fractional Gagliardo-Nirenberg-Sobolev inequality(1)‖f‖Wr,q(Ω)≲‖f‖Ws1,p1(Ω)θ‖f‖Ws2,p2(Ω)1−θ,∀f∈Ws1,p1(Ω)∩Ws2,p2(Ω). Here, s1,s2,r are non-negative numbers (not necessarily integers), 1≤p1,p2,q≤∞, and we assume, for some θ∈(0,1), the standard relations(2)r
ISSN:0022-1236
1096-0783
DOI:10.1016/j.jfa.2019.02.019