发表机构
Sanming University（三明大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文在加权Besov空间中证明了带显式权重依赖的Jackson型不等式，误差衰减由光滑度与维度比决定，并验证了指数最优性与局部化必要性。
AI 中文摘要
我们在具有Muckenhoupt权重的齐次加权Besov空间中，证明了对于由单位立方体的二进树上的小波展开恢复的函数，用指定数量的带限双正交小波系统项进行逼近的Jackson型不等式。误差衰减速率由光滑度与维度之比决定。显式常数具有闭式上界，权重仅通过Muckenhoupt特征值的显示幂次进入。一个极值族表明该速率的指数在类上不能增大，一个无权重例子表明局部化是必要的。
英文摘要
We prove a Jackson-type inequality for approximation by a prescribed number of terms of a band-limited biorthogonal wavelet system in homogeneous weighted Besov spaces with Muckenhoupt weights, on functions recovered from their wavelet expansion along the dyadic tree of the unit cube. The error decays at a rate set by the smoothness-to-dimension ratio. The explicit constant has a closed-form majorant, and the weight enters only through a displayed power of the Muckenhoupt characteristic. An extremal family shows that the exponent of this rate cannot be increased on the class, and an unweighted example shows that the localization is necessary.
