AI 中文总结
本文在一般巴拿赫格中研究线性 Kantorovich 型采样算子的逼近性质，在 Steklov 平均算子一致有界假设下建立相关估计，其框架无需空间平移不变，扩展了仅针对$L_p$空间的相关估计。
AI 中文摘要
本文研究环面$\boldsymbol{\top}$和实数轴$\boldsymbol{\textrm{R}}$上一般巴拿赫格$X$中线性 Kantorovich 型采样算子的逼近性质。在 Steklov 平均算子一致有界的自然假设下，我们建立了直接与逆逼近估计及强逆不等式。该框架不要求底空间具有平移不变性，从而覆盖了多种类型空间，扩展了此前主要针对勒贝格空间$L_p$的 Kantorovich 型算子估计。
英文摘要
This paper investigates the approximation properties of linear Kantorovich-type sampling operators in the setting of general Banach lattices $X$ on the torus $\mathbb{T}$ and the real line $\mathbb{R}$. Under a natural assumption on the uniform boundedness of the Steklov averaging operators, we establish direct and inverse approximation estimates, as well as strong converse inequalities. Our framework does not require the underlying spaces to be translation-invariant, thereby covering a wide variety of classes and extending the estimates for Kantorovich-type operators previously known primarily for Lebesgue spaces $L_p$.
