On the rate of convergence of ((||ƒ||p)¦(||ƒ||∞))p as p →∞

Lars Ole Ronnow Olsen

doi:10.1007/s00009-018-1295-5

On the rate of convergence of ((||ƒ||_p)¦(||ƒ||∞))^pas p →∞

Lars Ole Ronnow Olsen

Pure Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Let (X,ε,μ) be a measure space and let ƒ:X→ ℝ be a measurable function such that ||ƒ||_p_<∞for all p ≥ 1 and ||ƒ||_∞>0. In this paper, we describe the rate of convergence of ((||ƒ||_p)¦(||ƒ||∞))^pas p →∞.

Original language	English
Article number	11
Number of pages	10
Journal	Mediterranean Journal of Mathematics
Volume	16
Early online date	5 Jan 2019
DOIs	https://doi.org/10.1007/s00009-018-1295-5
Publication status	Published - Feb 2019

Keywords

Lp-norm
Rate of convergence

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10.1007/s00009-018-1295-5Licence: CC BY

Olsen2019_Article_OnTheRateOfConvergenceOfBigFra
© The Author(s) 2019. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
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Cite this

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abstract = "Let (X,ε,μ) be a measure space and let ƒ:X→ ℝ be a measurable function such that ||ƒ||p < ∞ for all p ≥ 1 and ||ƒ||∞ >0. In this paper, we describe the rate of convergence of ((||ƒ||p)¦(||ƒ||∞))p as p →∞.",

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AB - Let (X,ε,μ) be a measure space and let ƒ:X→ ℝ be a measurable function such that ||ƒ||p < ∞ for all p ≥ 1 and ||ƒ||∞ >0. In this paper, we describe the rate of convergence of ((||ƒ||p)¦(||ƒ||∞))p as p →∞.

KW - Lp-norm

KW - Rate of convergence

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