论文标题
Riesz变换的二元平均值产生的积分
An integral arising from dyadic average of Riesz transforms
论文作者
论文摘要
在S. petermichl，S。Treil和A. Volberg的工作中，明确构建了Riesz在任何维度上转换$ n \ geq 2 $，只要积分是非零的，只要二元式HAAR偏移的平均值即可获得。在论文中显示，当$ n = 2 $时，积分确实是非零（负），但对于$ n \ geq 3 $，非零属性仍未解决。在本文中，我们表明该积分为$ n = 3 $的非零（负）。我们证明的新颖性是积分不可或缺的分解，我们可以找到它们的封闭形式或证明上限。
In the work of S. Petermichl, S. Treil and A. Volberg it was explicitly constructed that the Riesz transforms in any dimension $n \geq 2$ can be obtained as an average of dyadic Haar shifts provided that an integral is nonzero. It was shown in the paper that when $n=2$, the integral is indeed nonzero (negative) but for $n \geq 3$ the nonzero property remains unsolved. In this paper we show that the integral is nonzero (negative) for $n=3$. The novelty in our proof is the delicate decompositions of the integral for which we can either find their closed forms or prove an upper bound.
