Abstract
For \(0 \lt q \le p\) we take \(L^\beta\)-averages over the Hölder inequality between the \(l^q\)-norm and the \(l^p\)-norm in \(\mathbb{R}^n\). We obtain precise limits as \(n\to\infty\) for the \(l^p\)-unit ball and, in case \(p\ge1\), also for the \(l^p\)-unit sphere, which coincide and are independent of \(\beta>0\). These are consequences of more general results on the asymptotic behavior of corresponding integrals over balls and spheres of certain bounded measurable functions.
Citation
Gerd Herzog. Peer Chr. Kunstmann. "Asymptotic Constants in Averaged Hölder Inequalities." Real Anal. Exchange 45 (2) 425 - 438, 2020. https://doi.org/10.14321/realanalexch.45.2.0425
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