Geodesic
Weighted multidimensional inequalities for monotone functions
Mathematica Bohemica, Tome 124 (1999) no. 2-3, pp. 329-335.

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We discuss the characterization of the inequality \biggl(\int_{{\Bbb R}^N_+} f^q u\biggr)^{1/q} \leq C \biggl(\int_{{\Bbb R}^N_+} f^p v \biggr)^{1/p},\quad0, p \infty, for monotone functions $f\geq0$ and nonnegative weights $u$ and $v$ and $N\geq1$. We prove a new multidimensional integral modular inequality for monotone functions. This inequality generalizes and unifies some recent results in one and several dimensions.
DOI : 10.21136/MB.1999.126258
Classification : 26A48, 26B25, 26B99, 26D15, 46E30
Keywords: integral inequalities; monotone functions; several variables; modular functions; convex functions; weakly convex functions; weighted $L^p$ spaces 
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Barza, Sorina; Persson, Lars-Erik. Weighted multidimensional inequalities for monotone functions. Mathematica Bohemica, Tome 124 (1999) no. 2-3, pp. 329-335. doi : 10.21136/MB.1999.126258. http://geodesic.mathdoc.fr/articles/10.21136/MB.1999.126258/

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