论文标题
离散的双Hilbert沿多项式表面转化
Discrete Double Hilbert Transforms Along Polynomial Surfaces
论文作者
论文摘要
我们在多项式$ p（T_1，T_2）$上获得了必要的条件，用于$ \ ell^{p} $与$ p（t）$相关的离散双hilbert变换的有限性，价格为$ 1 <p <\ p <\ infty $。该证明基于多参数圆方法处理$ | t_1 | \ not \ lot \ | t_2 | $从$ 1/t_1 $和$ 1/t_2 $产生的情况。
We obtain a necessary and sufficient condition on a polynomial $P(t_1,t_2)$ for the $\ell^{p}$ boundedness of the discrete double Hilbert transforms associated with $P(t)$ for $1 < p < \infty$. The proof is based on the multi-parameter circle method treating the cases of $|t_1|\not\approx |t_2|$ arising from $1/t_1$ and $1/t_2$.
