论文标题
BESOV类的Kolmogorov宽度$ B^1_ {1，θ} $和Octahedra的产品
Kolmogorov widths of Besov classes $B^1_{1,θ}$ and products of octahedra
论文作者
论文摘要
在本文中，我们找到了与$ W^1_1 $有关的kolmogorov宽度的衰减顺序（$ w^1_1 $的宽度的行为仍然未知）：$$ d_n（b^1_ {1，θ}} [0,1]，[0,1]，l_q [0,1] \ l_q [0,1] n^{ - 1/2} \ log^{\ max（\ frac12,1- \ frac {1}θ）} n，\ quad 2 <q <q <\ infty。 $$证明依赖于特殊规范的Octahedra产品的宽度（最多两个加权$ \ ell_q $ norms）。这将在$ \ ell_q^n $中概括B.S.〜Kashin的定理。
In this paper we find the orders of decay for Kolmogorov widths of some Besov classes related to $W^1_1$ (the behaviour of the widths for $W^1_1$ remains unknown): $$ d_n(B^1_{1,θ}[0,1],L_q[0,1])\asymp n^{-1/2}\log^{\max(\frac12,1-\frac{1}θ)}n,\quad 2<q<\infty. $$ The proof relies on the lower bound for widths of product of octahedra in a special norm (maximum of two weighted $\ell_q$ norms). This bound generalizes the theorem of B.S.~Kashin on widths of octahedra in $\ell_q^N$.
