MATHEMATICA BOHEMICA, Vol. 124, No. 2–3, pp. 329-335 (1999)

Weighted multidimensional inequalities for monotone functions

Sorina Barza, Lars-Erik Persson

Sorina Barza, Lars-Erik Persson, Department of Mathematics, Lulea University of Technology, S-97187 Lulea, Sweden, e-mails:,

Abstract: We discuss the characterization of the inequality $$ \biggl(\int_{{\Bbb R}^N_+} f^q u\biggr)^{1/q} \leq C \biggl(\int_{{\Bbb R}^N_+} f^p v \biggr)^{1/p},\quad0<q, p <\infty, $$ 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.

Keywords: integral inequalities, monotone functions, several variables, weighted $L^p$ spaces, modular functions, convex functions, weakly convex functions

Classification (MSC2000): 26D15, 26B99

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