论文标题
$ l^p $规律性用于海森伯格集团上的一类平均运营商
$L^p$ regularity for a class of averaging operators on the Heisenberg group
论文作者
论文摘要
我们证明$ l^p_ {comp} \ to l^p_ {s} $有界，用于在Heisenberg Group $ \ Mathbb {H}^1 $中通过$ l^2 $估算相关的振荡性积分和Bourgain Dememeter demplemere Encomelies conee conee conee的相关振荡性积分和Bourgain dememeter的相关估算。我们还构建了一个适合海森堡集团翻译的Sobolev空间，这些平均操作员映射了所有$ l^p $有限的功能。
We prove $L^p_{comp}\to L^p_{s}$ boundedness for averaging operators associated to a class of curves in the Heisenberg group $\mathbb{H}^1$ via $L^2$ estimates for related oscillatory integrals and Bourgain-Demeter decoupling inequalities on the cone. We also construct a Sobolev space adapted to translations on the Heisenberg group to which these averaging operators map all $L^p$ functions boundedly.
