论文标题
对均质组的粗糙奇异积分的定量加权估计值
Quantitative weighted estimates for rough singular integrals on homogeneous groups
论文作者
论文摘要
在本文中，我们研究了加权$ l^{p}（w）$有界（$ 1 <p <\ p <\ infty $和$ w $ a muckenhoupt $ a_ {p} $ a_ {p} $重量的单数积分，带有均匀的卷积内核$ k（x）$的同质组$ \ mathbb h $ of dimemension $ \ of dimemension $ \ of dimemention $ \ of dimemist $ k_0 $，$ k $对单位环的限制为平均零，对于某些$ q_ {0} <q \ leq \ infty $，}的$ q_ {0} $是$ q_ {0} $是固定常数，根据$ w $，$ q_ {0} <q \ leq \ infty $，}。我们获得了一个定量加权结合，这与Hytönen-roncal-tapiola在欧几里得环境中获得的绑定是一致的，对于$ l^{p}（w）$，该操作员在欧几里得设置中。与欧几里得环境中先前的结果相比，我们对内核和基础空间上的假设较弱。此外，我们研究了针对产品均匀谎言组的双参数粗糙奇异积分的定量加权结合。
In this paper, we study weighted $L^{p}(w)$ boundedness ($1<p<\infty$ and $w$ a Muckenhoupt $A_{p}$ weight) of singular integrals with homogeneous convolution kernel $K(x)$ on an arbitrary homogeneous group $\mathbb H$ of dimension $\mathbb{Q}$, {under the assumption that $K_0$, the restriction of $K$ to the unit annulus, is mean zero and $L^{q}$ integrable for some $q_{0}<q\leq \infty$,} where $q_{0}$ is a fixed constant depending on $w$. We obtain a quantitative weighted bound, which is consistent with the one obtained by Hytönen--Roncal--Tapiola in the Euclidean setting, for this operator on $L^{p}(w)$. Comparing to the previous results in the Euclidean setting, our assumptions on the kernel and on the underlying space are weaker. Moreover, we investigate the quantitative weighted bound for the bi-parameter rough singular integrals on product homogeneous Lie groups.
