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Sharp Marchaud and converse inequalities in Orlicz spaces

Authors:	Z Ditzian A V Prymak

Institution:	Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, Canada T6G 2G1 ; Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, Canada T6G 2G1

Abstract:	For spaces on $\mathbb{T}^d$ , $\mathbb{R}^d$ and $S^{d-1}$ , sharp versions of the classical Marchaud inequality are known. These results are extended here to Orlicz spaces (on $\mathbb{T}^d$ , $\mathbb{R}^d$ and $S^{d-1}$ ) for which $M(u^{1/q})$ is convex for some , $1<q\le2$ , where is the Orlicz function. Sharp converse inequalities for such spaces are deduced.

Keywords:	Sharp Marchaud inequality Orlicz spaces power-type $q$

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