Geodesic
On Optimal Banach Spaces Containing a Weight Cone of Monotone or Quasiconcave Functions
Matematičeskie zametki, Tome 98 (2015) no. 6, pp. 907-922

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Optimal (minimal) Banach spaces containing given cones of monotone or quasiconcave functions on the semiaxis from weighted Lebesgue spaces are described. Exact formulas for the norm of the optimal space are presented. All cases of the summation parameter are studied.
Keywords: optimal (minimal) Banach space, cone of monotone functions, cone of quasiconcave functions, weighted Lebesgue space, Sinnamon's lemma. 
@article{MZM_2015_98_6_a10,
     author = {V. D. Stepanov},
     title = {On {Optimal} {Banach} {Spaces} {Containing} a {Weight} {Cone} of {Monotone} or {Quasiconcave} {Functions}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {907--922},
     publisher = {mathdoc},
     volume = {98},
     number = {6},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2015_98_6_a10/}
}
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V. D. Stepanov. On Optimal Banach Spaces Containing a Weight Cone of Monotone or Quasiconcave Functions. Matematičeskie zametki, Tome 98 (2015) no. 6, pp. 907-922. http://geodesic.mathdoc.fr/item/MZM_2015_98_6_a10/