2026-06-27T22:58:45Zhttps://docta.ucm.es/rest/oai/requestoai:docta.ucm.es:20.500.14352/62562024-07-17T13:26:38Zcom_20.500.14352_14col_20.500.14352_15
Docta Complutense
author
Cobos Díaz, Fernando
author
Fernández-Cabrera Marín, Luz María
author
Martínez, Antón
2023-06-16T15:18:06Z
2023-06-16T15:18:06Z
2019-11-28
0362-546X
https://hdl.handle.net/20.500.14352/6256
https://www.journals.elsevier.com/nonlinear-analysis
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.
eng
On compactness results of Lions-Peetre type for bilinear operators
journal article
URL
https://docta.ucm.es/bitstreams/41fa2245-cbe5-4146-9294-5c7c1695c30b/download
File
MD5
5bae0e238c7df97f65ee9ea42e724946
285389
application/pdf
Cobos114pre.pdf
URL
https://docta.ucm.es/bitstreams/f1de0be1-8e85-4525-bac2-12f8a007cc80/download
File
MD5
1249c127f3d014c5c95513024f6a04f7
26443
text/plain
Cobos114pre.pdf.txt