RT Journal Article
T1 On compactness results of Lions-Peetre type for bilinear operators
A1 Cobos Díaz, Fernando
A1 Fernández-Cabrera Marín, Luz María
A1 Martínez, Antón
AB Let Ā = (A₀ , A₁) , B̄ = (B₀ , B₁) be Banach couples, let E be a Banach space and let T be a bilinear operator such that ||T(a, b)||ᴇ ≤ M[sub]j ||a||ᴀ[sub]j ||b||ʙ[sub]j for a ∈ A₀ ∩ A₁, b ∈ B₀ ∩ B₁, j = 0, 1. If T : A°[sub]j × B°[sub]j −→ E compactly for j = 0 or 1, we show that T may be uniquely extended to a compact bilinear operator from the complex interpolation spaces generated by Ā and B̄ to E. Furthermore, the corresponding result for the real method is given and we also study the case when E is replaced by a couple (E₀, E₁) of Banach function spaces on the same measure space.
PB Elsevier
SN 0362-546X
YR 2019
FD 2019-11-28
LK https://hdl.handle.net/20.500.14352/6256
UL https://hdl.handle.net/20.500.14352/6256
LA eng
NO Ministerio de Ciencia, Innovación y Universidades (España)/Fondo Europeo de Desarrollo Regional
DS Docta Complutense
RD 9 abr 2025