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Weighted multidimensional inequalities for monotone functions

Sorina BarzaLars-Erik Persson — 1999

Mathematica Bohemica

We discuss the characterization of the inequality (RN+ fq u)1/q C (RN+ fp v )1/p,   0<q, p <, for monotone functions f 0 and nonnegative weights u and v and N 1 . We prove a new multidimensional integral modular inequality for monotone functions. This inequality generalizes and unifies some recent results in one and several dimensions.

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