Geodesic
Some New Extrapolation Estimates for the Scale of $L_p$-Spaces
Funkcionalʹnyj analiz i ego priloženiâ, Tome 37 (2003) no. 3, pp. 73-77

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Using new extrapolation estimates for the $\mathcal{K}$- and $\mathcal{J}$-functionals of couples of limit spaces of the $L_p$-scale ($1$), we introduce a class of extrapolation functors. A characterization of this class via the real interpolation method permits one to obtain new equivalent expressions for the norms in symmetric spaces “close” to $L_\infty$ and $L_1$, which depend only on the $L_p$-norms of a function.
Keywords: Yano's extrapolation theorem, Peetre's $\mathcal{K}$- and $\mathcal{J}$-functionals, Banach couple, rearrangement invariant space, Orlicz space, Zygmund space, extrapolation functor, real interpolation method. 
@article{FAA_2003_37_3_a5,
     author = {S. V. Astashkin},
     title = {Some {New} {Extrapolation} {Estimates} for the {Scale} of $L_p${-Spaces}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {73--77},
     publisher = {mathdoc},
     volume = {37},
     number = {3},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2003_37_3_a5/}
}
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S. V. Astashkin. Some New Extrapolation Estimates for the Scale of $L_p$-Spaces. Funkcionalʹnyj analiz i ego priloženiâ, Tome 37 (2003) no. 3, pp. 73-77. http://geodesic.mathdoc.fr/item/FAA_2003_37_3_a5/