Geodesic
Extrapolation of operators acting into quasi-Banach spaces
Sbornik. Mathematics, Tome 207 (2016) no. 1, pp. 85-112

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Linear and sublinear operators acting from the scale of $L_p$ spaces to a certain fixed quasinormed space are considered. It is shown how the extrapolation construction proposed by Jawerth and Milman at the end of 1980s can be used to extend a bounded action of an operator from the $L_p$ scale to wider spaces. Theorems are proved which generalize Yano's extrapolation theorem to the case of a quasinormed target space. More precise results are obtained under additional conditions on the quasinorm. Bibliography: 35 titles.
Keywords: extrapolation of operators, Yano's theorem, symmetric space, Lorentz space
Mots-clés : quasi-Banach space. 
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     author = {K. V. Lykov},
     title = {Extrapolation of operators acting into {quasi-Banach} spaces},
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     url = {http://geodesic.mathdoc.fr/item/SM_2016_207_1_a3/}
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K. V. Lykov. Extrapolation of operators acting into quasi-Banach spaces. Sbornik. Mathematics, Tome 207 (2016) no. 1, pp. 85-112. http://geodesic.mathdoc.fr/item/SM_2016_207_1_a3/