Geodesic
The Real Interpolation Method on Couples of Intersections
Funkcionalʹnyj analiz i ego priloženiâ, Tome 40 (2006) no. 3, pp. 66-69 Cet article a éte moissonné depuis la source Math-Net.Ru

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Suppose that $(X_0,X_1)$ is a Banach couple, $X_0\cap X_1$ is dense in $X_0$ and $X_1$, $(X_0,X_1)_{\theta,q}$ ($0\theta1$, $1\le q\infty$) are the spaces of the real interpolation method, $\psi\in(X_0\cap X_1)^*$, $\psi\ne 0$, is a linear functional, $N=\operatorname{Ker}\psi$, and $N_i$ stands for $N$ with the norm inherited from $X_i$ ($i=0,1$). The following theorem is proved: the norms of the spaces $(N_0,N_1)_{\theta,q}$ and $(X_0,X_1)_{\theta,q}$ are equivalent on $N$ if and only if $\theta\in(0,\alpha)\cup(\beta_\infty,\alpha_0)\cup(\beta_0,\alpha_\infty)\cup(\beta,1)$, where $\alpha$, $\beta$, $\alpha_0$, $\beta_0$, $\alpha_\infty$, and $\beta_\infty$ are the dilation indices of the function $k(t)=\mathcal{K}(t,\psi;X_0^*,X_1^*)$.
Mots-clés : interpolation space
Keywords: interpolation of subspaces, interpolation of intersections, real interpolation method, $\mathcal{K}$-functional, dilation index of a function, weighted $L_p$-space. 
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S. V. Astashkin; P. Sunehag. The Real Interpolation Method on Couples of Intersections. Funkcionalʹnyj analiz i ego priloženiâ, Tome 40 (2006) no. 3, pp. 66-69. http://geodesic.mathdoc.fr/item/FAA_2006_40_3_a6/

[1] I. Berg, I. Lefstrem, Interpolyatsionnye prostranstva. Vvedenie, Mir, M., 1980 | MR

[2] Zh. L. Lions, E. Madzhenes, Neodnorodnye granichnye zadachi i ikh prilozheniya, Mir, M., 1971 | Zbl

[3] H. Triebel, Math. Nachr., 69 (1975), 57–60 | DOI | MR | Zbl

[4] L. Maligranda, Suppl. Rend. Circ. Mat. Palermo, 10 (1985), 113–118 | MR | Zbl

[5] R. Wallsten, Lecture Notes in Math., 1902, 1988, 410–419 | DOI | MR

[6] G. Pisier, Pacific J. Math., 155 (1992), 341–368 | DOI | MR | Zbl

[7] S. Janson, Arkiv Math., 31 (1993), 307–338 | DOI | MR | Zbl

[8] S. V. Kislyakov, Kuankhua Shu, Algebra i analiz, 8:4 (1996), 75–109 | MR | Zbl

[9] J. Löfström, Interpolation of subspaces, Technical report no. 10, Univ. of Göteborg, 1997

[10] S. Ivanov, N. Kalton, Algebra i analiz, 13:2 (2001), 93–115 | MR

[11] S. V. Astashkin, J. Math. Math. Sci., 25:7 (2001), 451–465 | DOI | MR | Zbl

[12] S. Kaijser, P. Sunehag, Function Spaces, Interpolation Theory and Related Topics (Lund 2000), de Gruyter, Berlin, 2002, 345–353 | MR | Zbl

[13] S. V. Astashkin, Funkts. analiz i ego pril., 39:2 (2005), 61–64 | DOI | MR | Zbl

[14] S. V. Astashkin, Algebra i analiz, 17:2 (2005), 33–69 | MR

[15] P. Sunehag, J. Approx. Theory, 130 (2004), 78–98 | DOI | MR | Zbl

[16] N. Krugljak, L. Maligranda, L.-E. Persson, Arkiv Mat., 37 (1999), 323–344 | DOI | MR | Zbl