Abstract
Let \((X,{\mathcal {E}},\mu )\) be a measure space and let \(f:X\rightarrow \mathbb R\) be a measurable function such that \(\Vert f\Vert _{p}<\infty \) for all \(p\ge 1\) and \(\Vert f\Vert _{\infty }>0\). In this paper, we describe the rate of convergence of \((\frac{\Vert f\Vert _{p}}{\Vert f\Vert _{\infty }})^{p}\) as \(p\rightarrow \infty \).
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Olsen, L. On the Rate of Convergence of \(\big (\frac{\Vert f\Vert _{p}}{\Vert f\Vert _{\infty }}\big )^{p}\) as \(p\rightarrow \infty \). Mediterr. J. Math. 16, 11 (2019). https://doi.org/10.1007/s00009-018-1295-5
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DOI: https://doi.org/10.1007/s00009-018-1295-5