- Tytuł:
- A Carlson type inequality with blocks and interpolation
- Autorzy:
-
Ya Kruglyak, Natan
Maligranda, Lech
Persson, Lars - Powiązania:
- https://bibliotekanauki.pl/articles/1292922.pdf
- Data publikacji:
- 1993
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
concavity
Carlson's inequality
blocks
interpolation
Peetre's interpolation functor
Calderón-Lozanovskiǐ construction - Opis:
- An inequality, which generalizes and unifies some recently proved Carlson type inequalities, is proved. The inequality contains a certain number of "blocks" and it is shown that these blocks are, in a sense, optimal and cannot be removed or essentially changed. The proof is based on a special equivalent representation of a concave function (see [6, pp. 320-325]). Our Carlson type inequality is used to characterize Peetre's interpolation functor $⟨⟩_{φ}$ (see [26]) and its Gagliardo closure on couples of functional Banach lattices in terms of the Calderón-Lozanovskiǐ construction. Our interest in this functor is inspired by the fact that if $φ = t^{θ}(0 < θ < 1)$, then, on couples of Banach lattices and their retracts, it coincides with the complex method (see [20], [27]) and, thus, it may be regarded as a "real version" of the complex method.
- Źródło:
-
Studia Mathematica; 1993, 104, 2; 161-180
0039-3223 - Pojawia się w:
- Studia Mathematica
- Dostawca treści:
- Biblioteka Nauki
Artykuł