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St. Petersburg Mathematical Journal

ISSN 1547-7371(online) ISSN 1061-0022(print)



Represensibility of cones of monotone functions in weighted Lebesgue spaces and extrapolation of operators on these cones

Authors: E. I. Berezhnoĭ and L. Maligranda
Translated by: S. V. Kislyakov
Original publication: Algebra i Analiz, tom 29 (2017), nomer 4.
Journal: St. Petersburg Math. J. 29 (2018), 545-574
MSC (2010): Primary 46E30, 46B20, 46B42
Published electronically: June 1, 2018
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Abstract: It is shown that a sublinear operator is bounded on the cone of monotone functions if and only if a certain new operator related to the one mentioned above is bounded on a certain ideal space defined constructively. This construction is used to provide new extrapolation theorems for operators on the cone in weighted Lebesgue spaces.

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Additional Information

E. I. Berezhnoĭ
Affiliation: P. G. Demidov Yaroslavl, State University, ul. Sovetskaya 14, 150000 Yaroslavl, Russia

L. Maligranda
Affiliation: Luleå University of Technology, S-971 87, Luleå, Sweden

Keywords: Weighted Lebesgue space, cone of monotone functions, extrapolation of operators
Received by editor(s): May 15, 2016
Published electronically: June 1, 2018
Additional Notes: Supported by RFBR (grant no. 14-01-00417)
Article copyright: © Copyright 2018 American Mathematical Society

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