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 Tr. Inst. Mat., 2014, Volume 22, Number 1, Pages 24–34 (Mi timb206)

Optimal Banach function space generated with the cone of nonnegative increasing functions

M. L. Goldmanab, P. P. Zabreikoab

a Peoples Friendship University of Russia, Moscow
b Belarusian State University, Minsk

Abstract: The article deals with the effective constructions for the optimal Banach ideal and symmetric spaces (of functions $f: [0,T]\to\mathbb{R}$) containing a cone of nonnegative and increasingly monotone functions with respect to the natural functional generated $L_p$-norm ($1\le p<\infty$). The first of these spaces turns out to be the space of measurable functions $f$ such that $\|f\|_{L_\infty(\cdot,T)}\in L_p(0,T)$; this space can be endowed with the norm $\| \|f\|_{L_\infty(\cdot,T)}\|f\|_{L_p(0,T)}$. The second coincides with the usual space $L_p$.

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UDC: 517.51

Citation: M. L. Goldman, P. P. Zabreiko, “Optimal Banach function space generated with the cone of nonnegative increasing functions”, Tr. Inst. Mat., 22:1 (2014), 24–34

Citation in format AMSBIB
\Bibitem{GolZab14} \by M.~L.~Goldman, P.~P.~Zabreiko \paper Optimal Banach function space generated with the cone of nonnegative increasing functions \jour Tr. Inst. Mat. \yr 2014 \vol 22 \issue 1 \pages 24--34 \mathnet{http://mi.mathnet.ru/timb206} 

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This publication is cited in the following articles:
1. I. V. Orlov, “Embedding of a Uniquely Divisible Abelian Semigroup In a Convex Cone”, Math. Notes, 102:3 (2017), 361–368
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