Cobos, Fernando and Cordeiro, José María and Martínez, Antón:
On interpolation of bilinear operators by methods associated to polygons
Bollettino dell'Unione Matematica Italiana Serie 8 2-B (1999), fasc. n.2, p. 319-330, Unione Matematica Italiana (English)
pdf (252 Kb), djvu (163 Kb). | MR1706592 | Zbl 0934.46022
Sunto
Stabiliamo teoremi di interpolazione bilineare per una combinazione dei metodi di $K$- e $J$-interpolazione associati ai poligoni, e per il $J$-metodo. Mostriamo che un simile risultato fallisce per il $K$-metodo, e diamo applicazioni all'interpolazione di spazi di operatori.
Referenze Bibliografiche
[1]
S. V.
ASTASHKIN
,
On interpolation of bilinear operators with a real method,
Mat. Zametki,
52 (
1992), 15-24. |
MR 1187708 |
Zbl 0798.46054[2]
J.
BERGH
-
J.
LÖFSTRÖM
,
«Interpolation Spaces. An Introduction»,
Springer, Berlin-Heidelberg-New York (
1976). |
MR 482275 |
Zbl 0344.46071[3]
F.
COBOS
-
P.
FERNÁNDEZ-MARTÍNEZ
,
A duality theorem for interpolation methods associated to polygons,
Proc. Amer. Math. Soc.
121, (
1994), 1093-1101. |
MR 1209420 |
Zbl 0806.46020[4]
F.
COBOS
-
P.
FERNÁNDEZ-MARTÍNEZ
-
A.
MARTÍNEZ
,
On reiteration and the behavior of weak compactness under certain interpolation methods,
Collect. Math. (to appear). |
MR 1701216 |
Zbl 0935.46060[5]
F.
COBOS
-
P.
FERNÁNDEZ-MARTÍNEZ
-
A.
MARTÍNEZ
-
Y.
RAYNAUD
,
On duality between $K$- and $J$-spaces,
Proc. Edinburgh Math. Soc. (to appear). |
Zbl 0921.46016[6]
F.
COBOS
-
P.
FERNÁNDEZ-MARTÍNEZ
-
T.
SCHONBEK
,
Norm estimates for interpolation methods defined by means of polygons,
J. Approx. Theory,
80 (
1995), 321-351. |
MR 1320157 |
Zbl 0922.46019[7]
F.
COBOS
-
J.
PEETRE
,
Interpolation of compact operators: The multidimensional case,
Proc. London Math. Soc.,
63 (
1991), 371-400. |
MR 1114514 |
Zbl 0702.46047[8]
M.
CWIKEL
-
S.
JANSON
,
Real and complex interpolation methods for finite and infinite families of Banach spaces,
Adv. Math.,
66 (
1987), 234-290. |
MR 915856 |
Zbl 0646.46070[9]
A.
FAVINI
,
Some results on interpolation of bilinear operators,
Boll. Un. Mat. Ital.,
15 (
1978), 170-181. |
MR 493413 |
Zbl 0377.46018[10]
D. L.
FERNANDEZ
,
Interpolation of $2^{d}$ Banach spaces and the Calderón spaces $X(E)$,
Proc. London Math. Soc.,
56 (
1988), 143-162. |
MR 915534 |
Zbl 0662.46077[11]
S.
JANSON
,
On interpolation of multi-linear operators, in
Function Spaces and Applications, Proceedings, Lund 1986,
Lect. Notes Math.,
1302 (
1988), 290-302. |
MR 942274 |
Zbl 0827.46062[13]
J.
PEETRE
,
Paracommutators and minimal spaces, in
Operators and Funtion Theory, Proceedings of the NATO Advanced Study Institute on Operators and Function Theory, Lancaster,
1984, ed. S. C. Power,
Reidel, Dordrecht (
1985), 163-223. |
MR 810447 |
Zbl 0571.46019[14]
G.
SPARR
,
Interpolation of several Banach spaces,
Ann. Math. Pura Appl.,
99 (
1974), 247-316. |
MR 372641 |
Zbl 0282.46022[15]
H.
TRIEBEL
,
Interpolation Theory, Function Spaces, Differential Operators,
North-Holland, Amsterdam (
1978). |
MR 503903 |
Zbl 0387.46032[16]
M.
ZAFRAN
,
A multilinear interpolation theorem,
Studia Math.,
62 (
1978), 107-124. |
MR 499959 |
Zbl 0389.46025