Interpolation properties of scales of Banach spaces
Matematičeskie zametki, Tome 80 (2006) no. 6, pp. 803-813
Citer cet article
Voir la notice de l'article provenant de la source Math-Net.Ru
It is shown that any interpolation scales joining weight spaces $L_p$ or similar spaces have many remarkable properties. Not only are such scales intrinsically interpolation scales, but an analog of the Arazy–Cwikel theorem describing interpolation spaces between the spaces from the scale is valid.
[1] I. Berg, I. Lëfstrëm, Interpolyatsionnye prostranstva. Vvedenie, Mir, M., 1980 | MR | Zbl
[2] S. G. Krein, Yu. I. Petunin, E. M. Semenov, Interpolyatsiya lineinykh operatorov, Nauka, M., 1978 | MR | Zbl
[3] Y. Arazy, M. Cwikel, “A new characterization of the interpolation spaces between $L_p$ and $L_q$”, Math. Scand., 55:2 (1984), 253–270 | MR | Zbl
[4] G. Sparr, “Interpolation of weighted $L_p$ spaces”, Studia Math., 62 (1978), 229–271 | MR | Zbl
[5] V. I. Ovchinnikov, “The method of orbits in interpolation theory”, Math. Rep. Ser. 1, 1:2 (1984), 349–515 | MR | Zbl