DISCREPANCY OF GENERALIZED HAMMERSLEY TYPE POINT SETS IN BESOV SPACES WITH DOMINATING MIXED SMOOTHNESS
DISCREPANCY OF GENERALIZED HAMMERSLEY TYPE POINT SETS IN BESOV SPACES WITH DOMINATING MIXED SMOOTHNESS
复制标题
混合光滑占主导地位的Besov空间中广义Hammersley型点集的差异
DOI：
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
Lev Markhasin
中科院分区：
文献类型：
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作者：
Lev Markhasin
已知对称化的Hammersley点集对于差异函数的L2-范数实现最佳可能速率。此外，已知Besov空间中具有支配混合光滑性的范数的下界。本文证明了一类广义Hammersley型点集渐近达到已知的Besov范数下界。该证明使用Haar系统的b-adic推广。这一结果可以看作是对任意维证明的一个准备。
The symmetrized Hammersley point set is known to achieve the best possible rate for the L2-norm of the discrepancy function. Also lower bounds for the norm in Besov spaces with 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.