On the equivalence between trace and capacitary inequalities for the abstract contractive space of Bessel potentials

Autor(en): Ben Amor, A
Stichwörter: DIRICHLET FORMS; Mathematics; OPERATORS; SOBOLEV
Erscheinungsdatum: 2005
Herausgeber: OSAKA JOURNAL OF MATHEMATICS
Journal: OSAKA JOURNAL OF MATHEMATICS
Volumen: 42
Ausgabe: 1
Startseite: 11
Seitenende: 26
Zusammenfassung: 
Let F-r,F-p = V-r,V-p (L-p(X,m)) be the abstract space of Bessel potentials and mu a positive smooth Radon measure on X. For 2 <= p <= q < infinity, we give necessary and sufficient criteria for the boundedness of V-r,V-p from L-p(X, m) into L-p(X, mu), provided F-r,F-p is contractive. Among others, we shall prove that the boundedness is equivalent to a capacitary type inequality. Further we give necessary and sufficient conditions for F-r,F-p to be compactly embedded in L-q(mu). Our method relies essentially on establishing a capacitary strong type inequality.
ISSN: 00306126

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