论文标题
Nikolskii-Type不平等假设下的$ l^p $ norms的marcinkiewicz-type离散化
Marcinkiewicz-type discretization of $L^p$-norms under the Nikolskii-type inequality assumption
论文作者
论文摘要
本文研究了$ l^p（μ）$的子空间的积分规范的抽样离散问题。在某些Nikolskii-Type不等式有效的子空间上获得了几乎接近最佳结果。规范的离散化问题与概率问题有关，即通过采样的高维随机矢量的近似值近似。作为我们方法的副产品，我们完善了O. gu $ \ cucute {e} $ don and M. Rudelson的结果。特别是，所获得的改进恢复了J. Bourgain，J。Lindenstrauss和V. Milman的定理，内容涉及$ l^p [0，1] $的有限尺寸子空间的嵌入到$ \ ell_p^m $中。本文中的证据使用了R. Van Handel的链接技术的最新发展。
The paper studies the sampling discretization problem for integral norms on subspaces of $L^p(μ)$. Several close to optimal results are obtained on subspaces for which certain Nikolskii-type inequality is valid. The problem of norms discretization is connected with the probabilistic question about the approximation with high probability of marginals of a high dimensional random vector by sampling. As a byproduct of our approach we refine the result of O. Gu$\acute{e}$don and M. Rudelson concerning the approximation of marginals. In particular, the obtained improvement recovers a theorem of J. Bourgain, J. Lindenstrauss, and V. Milman concerning embeddings of finite dimensional subspaces of $L^p[0, 1]$ into $\ell_p^m$. The proofs in the paper use the recent developments of the chaining technique by R. van Handel.
