Besov空间中广义Hammersley型点集在主导混合光滑性下的差异
Discrepancy of generalized Hammersley type point sets in Besov spaces of dominating mixed smoothness
AI总结：
本文证明了一类广义Hammersley型点集在Besov范数下渐近达到已知下界，使用b-adic Haar系统推广进行证明。
摘要：
对称化的Hammersley点集已知在差异函数的$L_2$范数下达到最佳可能速率。此外，在主导混合光滑性的Besov空间中，范数的下界也是已知的。本文证明了一大类点集（Hammersley型点集的推广）渐近达到Besov范数的已知下界。证明使用了Haar系统的$b$-adic推广。该结果可视为任意维数证明的准备。
英文摘要：
The symmetrized Hammersley point set is known to achieve the best possible rate for the $L_2$-norm of the discrepancy function. Also lower bounds for the norm in Besov spaces of dominating mixed smoothness are known. In this paper a large class of point sets which are generalizations of the Hammersley type point sets are proved to asymptotically achieve the known lower bound of the Besov norm. The proof uses a $b$-adic generalization of the Haar system. This result can be regarded as a preparation for the proof in arbitrary dimension.
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