Geodesic
Extrapolation properties of the~scale of~$L_p$-spaces
Sbornik. Mathematics, Tome 194 (2003) no. 6, pp. 813-832

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A new class of extrapolation functors on the scale of $L_p$-spaces $(1$ is introduced, allowing one to take for its “limiting spaces” two symmetric spaces “close” to $L_\infty$ and $L_1$. Crucial here are the extrapolation relations for the Peetre $\mathscr K$- and $\mathscr J$-functionals for the Banach couples $(L_\infty,\operatorname{Exp} L^\beta)$ and $(L_1,L(\log L)^{1/\beta})$, respectively $(\operatorname{Exp} L^\beta$ and $L(\log L)^{1/\beta}$, $\beta>0$, are Zygmund spaces). The real method of operator interpolation is used. 
@article{SM_2003_194_6_a1,
     author = {S. V. Astashkin},
     title = {Extrapolation properties of the~scale of~$L_p$-spaces},
     journal = {Sbornik. Mathematics},
     pages = {813--832},
     publisher = {mathdoc},
     volume = {194},
     number = {6},
     year = {2003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2003_194_6_a1/}
}
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S. V. Astashkin. Extrapolation properties of the~scale of~$L_p$-spaces. Sbornik. Mathematics, Tome 194 (2003) no. 6, pp. 813-832. http://geodesic.mathdoc.fr/item/SM_2003_194_6_a1/