Sharp Marchaud and converse inequalities in Orlicz spaces

Ditzian, Z.; Prymak, A.

doi:10.1090/S0002-9939-06-08682-5

Sharp Marchaud and converse inequalities in Orlicz spaces
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by Z. Ditzian and A. V. Prymak PDF

Proc. Amer. Math. Soc. 135 (2007), 1115-1121 Request permission

Abstract:

For $L_p$ 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 $q$, $1<q\le 2$, where $M(u)$ is the Orlicz function. Sharp converse inequalities for such spaces are deduced.

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