论文标题
奇数最大riesz的无维度$ l^p $估计根据riesz变换而变换
Dimension-free $L^p$ estimates for odd order maximal Riesz transforms in terms of the Riesz transforms
论文作者
论文摘要
我们证明了一个无维$ l^p（\ mathbb {r}^d）$，$ 1 <p <\ infty $，根据相应的riesz变换而言，最大riesz向量估算了奇数的最大riesz向量。这意味着无尺寸的$ l^p（\ mathbb {r}^d）$估算最大riesz向量的估计，从输入函数来转换。我们还给出了固定订单时$ p $的依赖关系的明确估计。还获得了无尺寸估计值的奇数riesz变换，并具有改进的常数估计值。这些结果是J. Mateu，J。Orobitg，C。Pérez和J. Verdera的工作的无维度扩展。我们的证明包括分解和平均程序，然后是旋转方法的不明确应用。
We prove a dimension-free $L^p(\mathbb{R}^d)$, $1<p<\infty$, estimate for the vector of maximal Riesz transforms of odd order in terms of the corresponding Riesz transforms. This implies a dimension-free $L^p(\mathbb{R}^d)$ estimate for the vector of maximal Riesz transforms in terms of the input function. We also give explicit estimates for the dependencies of the constants on $p$ when the order is fixed. Analogous dimension-free estimates are also obtained for single Riesz transforms of odd orders with an improved estimate of the constants. These results are a dimension-free extension of the work of J. Mateu, J. Orobitg, C. Pérez, and J. Verdera. Our proof consists of factorization and averaging procedures, followed by a non-obvious application of the method of rotations.
