多变量抽样Kantorovich算子：Orlicz空间中的定量估计

IF 1.1 Q1 MATHEMATICS Constructive Mathematical Analysis Pub Date : 2021-02-16 DOI:10.33205/CMA.876890

L. Angeloni, N. Çetin, D. Costarelli, A. R. Sambucini, G. Vinti

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引用次数: 10

摘要

本文利用Orlicz空间的一般设置中的连续模，建立了多元采样Kantorovich算子的定量估计。因此，在函数属于合适的Lipschitz类的情况下，可以获得收敛的定性阶。在L^p-空间的特定例子中，使用直接方法，我们获得了比从一般情况中推导出的估计更清晰的估计。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Multivariate sampling Kantorovich operators: quantitative estimates in Orlicz spaces

In this paper, we establish a quantitative estimate for multivariate sampling Kantorovich operators by means of the modulus of continuity in the general setting of Orlicz spaces. As a consequence, the qualitative order of convergence can be obtained, in case of functions belonging to suitable Lipschitz classes. In the particular instance of L^p-spaces, using a direct approach, we obtain a sharper estimate than that one that can be deduced from the general case.

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