Mixed means and inequalities of Hardy and Levin-Cochran-Lee type for multidimensional balls

Čižmešija, Aleksandra; Pečarić, Josip; Perić, Ivan

doi:10.1090/S0002-9939-99-05408-8

Mixed means and inequalities of Hardy and Levin-Cochran-Lee type for multidimensional balls
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by Aleksandra Čižmešija, Josip Pečarić and Ivan Perić PDF

Proc. Amer. Math. Soc. 128 (2000), 2543-2552 Request permission

Abstract:

Integral means of arbitrary order, with power weights and their companion means, where the integrals are taken over balls in $\mathbf { R}^n$ centered at the origin, are introduced and related mixed-means inequalities are derived. These relations are then used in obtaining Hardy and Levin–Cochran–Lee inequalities and their companion results for $n$-dimensional balls. Finally, the best possible constants for these inequalities are obtained.

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