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Sbornik: Mathematics, 2016, Volume 207, Issue 1, Pages 85–112
DOI: https://doi.org/10.1070/SM8441 (Mi sm8441) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Extrapolation of operators acting into quasi-Banach spaces

K. V. Lykovabc

a Samara State University
b S. P. Korolyov Samara State Aerospace University
c Image Processing Systems Institute, Samara
English version PDF (588 kB) Citations (1) Russian version article
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DOI: https://doi.org/10.1070/SM8441
Abstract: 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, quasi-Banach space.
Funding agency Grant number
Russian Foundation for Basic Research 14-01-31452-мол-а
Ministry of Education and Science of the Russian Federation 02.В49.21.0005
204
This research was supported by the Russian Foundation for Basic Research (grant no. 14-01-31452-mol-a) and the Ministry of Education and Science of the Russian Federation (grant nos. 02.B49.21.0005, GZ204).
Received: 06.11.2014 and 21.08.2015
Bibliographic databases:
Document Type: Article
UDC: 517.982+517.983+517.988
MSC: Primary 46E30; Secondary 46B70, 46M35
Language: English
Original paper language: Russian
Citation: K. V. Lykov, “Extrapolation of operators acting into quasi-Banach spaces”, Sb. Math., 207:1 (2016), 85–112
Citation in format AMSBIB
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\paper Extrapolation of operators acting into quasi-Banach spaces
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\issue 1
\pages 85--112
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    References:78
    First page:35
     
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