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

Berezhnoĭ, E.; Maligranda, L.

doi:10.1090/spmj/1506

Represensibility of cones of monotone functions in weighted Lebesgue spaces and extrapolation of operators on these cones
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by E. I. Berezhnoĭ and L. Maligranda
Translated by: S. V. Kislyakov

St. Petersburg Math. J. 29 (2018), 545-574

DOI: https://doi.org/10.1090/spmj/1506

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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